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HAMILTON
LECTURES ON
,;',';/,;^PHYSlCS AND ,OGIC
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LECTURES
LOGIC
SIE WILLIAM HAMILTON, BAET.
EDITED BY THE
REV. H. L. MANSEL, B.D., LL.D.
AVNpr.nTE PR0KR59OR OK MORAT, AND MRTAPIIVSICAI, nill.OSnFUV, OXKOP
AND
JOHN VEITCH, M.A.
PROFESSOR OF LOGIC AND RUKTOniC IN THK UNIVEBSITV OP GLASOOW
VOL. II.
SECOND EDITION, EEVISED
WILLIAM BLACKWOOD AND SONS
s^ EDINBUEGH AND LONDON
^s^v MDCCCLXVI
The PJf/ht of Translation is referred
CONTENTS OF VOL. 11.
LECTUEE XXIV.
PURE LOGIC.
Page
PART II. METHODOLOGY. — SECTION I. METHOD IN GENERAL.
— SECTION II. METHOD IN SPECIAL, OR LOGICAL ME-
THODOLOGY.— I. DOCTRINE OF DEFINITION, . . 1
LECTUEE XXV.
METHODOLOGY.
LOGICAL METHODOLOGY. — II. DOCTRINE OF DIVISION, . 22
LECTUEE XXVL
LOGICAL METHODOLOGY. — III. DOCTRINE OF PROBATION, . 37
LECTUEE XXVIL
MODIFIED LOGIC.
PART I. MODIFIED STOICHEIOLOGY. — SECTION I. DOCTRINE
OF TRUTH AND ERROR. — TRUTH — ITS CHARACTER AND
KINDS, 60
LECTUEE XXVIIL
MODIFIED STOICHEIOLOGY.
SECTION I. DOCTRINE OF TRUTH AND ERROR. — SECTION II.
ERROR — ITS CAUSES AND REMEDIES. — A. GENERAL
CIRCUMSTANCES— SOCIETY, 75
viii CONTENTS.
LECTURE XXIX.
Paoe
ERROR— ITS CAUSES AND REMEDIES.— A. GENERAL CIRCUM-
STANCES — SOCIETY. — B. AS IN POWERS OF COGNITION,
FEELING, AND DESIRE. — L AFFECTIONS — PRECIPITANCY
— SLOTH — HOPE AND FEAR — SELF-LOVE, ... 89
LECTURE XXX.
ERROR — ITS CAUSES AND REMEDIES. — B. AS IN THE COG-
NITIONS, FEELINGS, AND DESIRES. — II. WEAKNESS AND
DISPROPORTIONED STRENGTH OF THE FACULTIES OF
KNOWLEDGE, 109
LECTURE XXXL
ERROR — ITS CAUSES AND REMEDIES. — C. LANGUAGE. — D.
OBJECTS OF KNOWLEDGE, 140
LECTURE XXXIL
MODIFIED METHODOLOGY.
SECTION I. OF THE ACQUISITION AND PERFECTING OF KNOW-
LEDGE. — I. EXPERIENCE. — A. PERSONAL : — OBSERVATION
— INDUCTION AND ANALOGY, 152
LECTURE XXXIIL
OF THE ACQUISITION AND PERFECTING OF KNOWLEDGE. —
I. EXPERIENCE.— B. FOREIGN: — ORAL TESTIMONY — ITS
CREDIBILITY, 175
LECTURE XXXIV.
OF THE ACQUISITION AND PERFECTING OF KNOWLEDGE. —
I. EXPERIENCE. — B, FOREIGN : RECORDED TESTIMONY
AND WRITINGS IN GENERAL. — 11. SPECULATION, . . 191
CONTENTS. IX
LECTURE XXXV.
Page
OF THE ACQUISITION AND PEKFECTING OF KNOWLEDGE. —
III. COMMUNICATION OF KNOWLEDGE. — A. INSTKUCTION
— 0£AL AND WKITTEN. — B. CONFERENCE — DIALOGUE
AND DISPUTATION, 204
APPENDIX.
I. — THE CHARACTER AND COMPREHENSION OF LOGIC — A
FRAGMENT, 229
II. — GENUS OF LOGIC, 233
III. — DIVISIONS, VARIETIES, AND CONTENTS OF LOGIC, . 239
IV. — NOTE OF LOGICAL TREATISES RECOMMENDED BY SIR
WILLIAM HAMILTON TO HIS CLASS, .... 244
V. — LAWS OF THOUGHT, 246
VI. — NEW ANALYTIC OF LOGICAL FORMS — GENERAL RE-
SULTS — FRAGMENTS.
{a) EXTRACT FROM PROSPECTUS OF ' ' ESSAY TOWARDS A NEW
ANALYTIC OF LOGICAL FORMS," .... 251
(b) LOGIC, — ITS POSTULATES, . . . . .254
(c) QUANTIFICATION OF PREDICATE,— IMMEDIATE INFERENCE,
— CONVERSION, — OPPOSITION, .... 257
(d) APPLICATION OF DOCTRINE OF QUANTIFIED PREDICATE TO
PROPOSITIONS, ...... 279
(c) APPLICATION OF DOCTRINE OF QUANTIFIED PREDICATE TO
SYLLOGISMS, ...... 290
(/) OBJECTIONS TO THE DOCTRINE OF A QUANTIFIED PREDI-,
CATE CONSIDERED, ..... 296
ig) HISTORICAL NOTICES OF DOCTRINE OF QUANTIFIED PRE-
DICATE, ....... 305
VII. — CANONS OF SYLLOGISM ; GENERAL HISTORICAL NO-
TICES AND CRITICISM.
A. HISTORICAL NOTICES.
(a) FUNDAMENTAL LAWS OF SYLLOGISM — QUOTATIONS, . 324
(b) FUNDAMENTAL LAWS OF SYLLOGISM — REFERENCES, . 346
(c) ENUNCIATIONS OF THE HIGHER LAWS OF SYLLOGISM, . 348
X CONTENTS.
VII. — CANONS OF SYLLOGISM — continued.
Page
{d) OBJECTIONS TO THE DICTUM DE OMNI ET NULLO, . 350
(c) GENERAL LAWS OF SYLLOGISM IN VERSE, . . . 350
(/) SPECIAL LAWS OF SYLLOGISM IN VERSE, . . . 351
B. CRITICISM.
(a) CRITICISM OF THE SPECIAL LAWS OF SYLLOGISM, . 352
{b) LAWS OF SECOND FIGURE, ..... 355
(c) author's supreme CANONS OF CATEGORICAL SYLLOGISMS, 357
(d) ULTRA-TOTAL QUANTIFICATION OF MIDDLE TERM, . 358
VIII. — INDUCTION AND EXAMPLE.
(a) QUOTATIONS FROM AUTHORS, .... 365
(S) MATERIAL INDUCTION, ..... 375
IX. — HYPOTHETICAL AND DISJUNCTIVE REASONING — IM-
MEDIATE INFERENCE.
A. author's DOCTRINE— FRAGMENTS, .... 376
B. HISTORICAL NOTICES, ..... 395
X.— SORITES, 403
XI. — SYLLOGISM.
A. ITS ENOUNCEMENT — ANALYTIC AND SYNTHETIC— ORDER OF
PREMISES.
(a) ENOUNCEMENT OF SYLLOGISM, . . . 406
(b) ORDER OF PREMISES, .... 409
B. FIGURE — UNFIGURED AND FIGURED SYLLOGISM.
(a) CONTRAST AND COMPARISON OF THE VARIOUS KINDS
OF FORMAL SYLLOGISM — DIFFERENCE OF FIGURE
ACCIDENTAL, ...... 412
{b) DOUBLE CONCLUSION IN SECOND AND THIRD FIGURES, 414
C. HISTORICAL NOTICES REGARDING FIGURE OF SYLLOGISM, . 421
D. SYLLOGISTIC MOODS.
(a) DIRECT AND INDIRECT MOODS, . . . 458
(b) INDIRECT MOODS OF SECOND AND THIRD FIGURES, 464
(c) NEW MOODS — NOTES UPON TABLE OF SYLLOGISMS, . 466
XII. — LOGICAL NOTATION.
(a) LAMBERT'S LINEAR NOTATION, . . . 469
(b) NOTATION BY MAASS, .... 472
(c) author's scheme of NOTATION — NO. I. LINEAR, . 473
{d) author's scheme of notation— UNFIGURED AND
FIGURED SYLLOGISM — NO. II., . . . 477
(f) author's scheme of notation — FIGURED SYLLO-
GISM — TABLE OF MOODS — NO. III., . . 485
LECTURES ON LOGIC.
LECTURE XXIV.
PURE LOGIC.
PART II. METHODOLOGY.
SECTION I. METHOD IN GENERAL.
SECTION II. METHOD IN SPECIAL, OR LOGICAL
METHODOLOGY.
I. DOCTRINE OF DEFINITION.
Gentlemen, — We concluded, in our last Lecture, the lect.
XXIV.
consideration of Syllogisms, viewed as Incorrect or '-
False ; in other words, the doctrine of Fallacies, in so JJ^'j!*"^'
far as the fallacy lies within a single syllogism. This,
however, you will notice, does not exhaust the consider-
ation of fallacy in general, for there are various species
of false reasoning which may affect a whole train of
syllogisms. These, — of which the Petitio P7nnci2Jii,
the Ignoratio Elenchi, the Circidus, and the Saltiis m
Concludendo, are the principal, — will be appropriately
considered in the sequel, when we come to treat of the
Doctrine of Probation or Demonstration. With Fal-
lacies terminated the one Great Division of Pure Logic,
— the Doctrine of Elements, or Stoicheiology, — and I
VOL. II. A
LECTURES ON LOGIC.
LECT. opentlieotlierGreat Division, — the Doctrine of Method,
XXIV
or Methodology, — with the following paragraph.
Par. Lxxx. IF LXXX. A Sciouce is a complement of cog-
Method in . . , . . . /» -n 11
genenij. mtions, havmg, m pomt oi i*orm, the character
of Logical Perfection ; in point of Matter, the
character of Real Truth.
The constituent attributes of Logical Perfec-
tion are the Perspicuity, the Completeness, the
Harmony, of Knowledge. But the Perspicuity,
Completeness, and Harmony of our cognitions
are, for the human mind, possible only through
Method.
Method in general denotes a procedure in the
treatment of an object, conducted according to
determinate rules. Method, in reference to Sci-
ence, denotes, therefore, the arrangement and ela-
boration of cognitions according to definite rules,
with the view of conferrino; on these a Looical
Perfection. The Methods by which we proceed
ill the treatment of the objects of our knowledge
are two ; or rather Method, considered in its inte-
grity, consists of two processes, — Analysis and
Synthesis.
1. The Analytic or Regressive ; — in which, de-
parting from the individual and the determined,
we ascend always to the more and more general,
in order finally to attain to ultimate principles.
IL The Synthetic or Progressive ; — in which
we depart from principles or universals, and from
these descend to the determined and the indi-
vidual.
Through the former we investigate and ascer-
tain the reality of the several objects of science ;
LECTURES ON LOGIC. 3
tliroiio-li tlie latter we conuect the fragments of lect.
. XXIV
our knowledge into the unity of a system. — '-
In its Stoicheiology or Doctrine of Elements, Logic Expiica-
considers the conditions of possible thought : for thought Possibility
can only be exerted under the general laws of Identity, faction of
Contradiction, Excluded Middle, and Keason and Con- "''^^'*'
sequent ; and through the general forms of Concepts,
Judgments, and Keasonings. These, therefore, may
be said to constitute the Elements of thought. But
we may consider thought not merely as existing, but
as existing Avell ; that is, we may consider it not only
in its possil^ility, but in its perfection : and this per-
fection, in so far as it is dependent on the form of
thinking, is as much the object-matter of Logic as the
mere possibility of thinking. Now that part of Logic
which is conversant with the Perfection, — with the
Well-being, of thought, is the Doctrine of Method, —
Methodology.
Method in general is the regulated procedure to- Method in
-, .-,■,. -i ■■ general, —
wards a certain end ; that is, a progress governed by what.
rules which guide us by the shortest way straight
towards a certain point, and guard us against devi-
ous aberrations." Now the end of thought is truth, —
knowledge, — science, — expressions which may here be
considered as convertible. Science may, therefore, be Sciences-
regarded as the perfection of thought, and to the
a [On Method, see Alex. ApUrod., Peter John Nunnesius, De (Jonstita-
In Anal. Prior. ,i.^'^,A\A.\52Q. Am- flone Artis Dialecticce,j). iZetseq.,ed.
mon'ms, In P^'omn. Porphyrii,i. 21b, 1554, with relative commentary. Tim-
Aid. 1546. Philoponus, In An. Prior., pier, Systema Logicce, L. iv. c. viii. p.
f. 4. InAn.Post.,t9i. Eustratius, /h 716 et seq. G. Bownam, Commentarii
^n.Po.s?.,fF.lb,53'\ See also Molinscus, in P. Raini Dialecticam, L. ii. c. 17,
Zabarella, Nunnesius, Timpler, Dow- p. 472 et seq. On the distinction be-
nam.] [MolinsiuB, Logica, L.ii.,i)e ilfe- tween Method and Order, see Lectures
thodo, -p. 2i5 et seq. Zabarella, O/Jera on Metap}iysics,Yo\. i, lect. vi. p. 96,
Logica, De Methndis, L. i. c. 2, p. 134. and note. — Ed.]
4 LECTURES ON LOGIC.
LECT. accomplislimeiit of tliis perfection the Metliodology of
1 L. Logic must be accommodatecl and conducive. But
Science, that is, a system of true or certain knowledge,
Its pcrfec- supposes two couditions. Of these the first has a re-
i.mi anT latiou to thc knowing subject, and supposes that w^hat
is known is known clearly and distinctly, completely,
and in connection. The second has a relation to the
objects known, and supposes that what is known has
a true or real existence. The former of these consti-
tutes the Formal Perfection of science, the latter is the
Material.
Logic takes Now, as Logic is a science exclusively conversant
only the""" about thc fomi of thought, it is evident that of these
fecUon oT two couditious, — of these two elements, of science or
perfect thinking, Logic can only take into account the
formal perfection, which may, therefore, be distinc-
tively denominated the logical perfection of thought.
Logical Logical Methodology will, therefore, be the exposition
o!oj?y°— of the rules and ways by which we attain the formal
or logical perfection of thought.
Method iu B^it Method, considered in general, — considered in
Mstr™ two' i^s unrestricted universality, — consists of two processes,
.nmUom-" correlative and complementary of each other. For
jlocesses,- ^^ procccds either from the whole to the parts, or from
™Tsyn- the parts to the whole. As proceeding from the whole
to the parts, that is, as resolving, as unloosing, a com-
plex totality into its constituent elements, it is Ana-
lytic ; as proceeding from the parts to the whole, that
is, as recomposing constituent elements into their
complex totality, it is Synthetic. These two processes
are not, in strict propriety, two several methods, but
together constitute only a single method. Each alone
is imperfect : — each is conditioned or consummated by
tliesis
LECTURES ON LOGIC. o
the other : and, as I formerly observed," Analysis and lect.
•^ 111 XXIV.
Synthesis are as necessary to themselves and to the
life of science, as expiration and inspiration in connec-
tion are necessary to each other and to the possibility
of animal existence.
It is here proper to make you aware of the confusion Confusion
T . . P T ^^ regard to
which prevails in regard to the application of the terms the appiica-
■"■ ' Q . f. . tion of the
Analysis 2(iidi Synthesis.^ It is manifest, m general, terms Ana-
-. • lysis Riici
from the meaning of the words, that the term afialysis Synthesis.
can only be applied to the separation of a whole into
its parts, and that the term synthesis can only be ap-
plied to the collection of parts into a whole. So far,
no ambiguity is possible, — no room is left for abuse.
But you are aware that there are different kinds of These couu-
f 1 1 1 T 1 **'" pi'ocesses
whole and parts ; and that some of the wholes, like as applied
Ti/T to the coun-
the whole of Comprehension, (called also the ikZeto- ter wholes
1^ • /nil of Compre-
physical), and the whole of Extension, (called also hension and
'^ "^ . , , . • p 1 1 Extension,
the Logical), are in the inverse ratio of each other : so correspond
a See Lectures on Metaphysics, vol. particulars to uuiversals ; other logi-
i. p. 99. — Ed. cians generally the reverse.] — [See
/3 [Zabarella, Opera Logica, Lihcr de his Prcvcepta Phil. Loyicce, P. III. c,
Reyressu, pp. 481, 489. See also, In i. §3, p. 84, 1781. — " Mentem suapte
Anal. Poster., L. ii. text 81, pp. 1212, natura Syntheticam Methodum sequi,
1213. MolinjBus, Lo/jica, L. ii. Ap- eaque ad universales ideas pervenire.
peudix, p. 241 et seq., who notices .... Contrarium est iter Ana-
that both the Analytic and Synthetic lyticse Methodi, quse ab universalibus
order may proceed from the general initium ducit et ad peculiaria pro-
to the particular. See also to the greditur, dividendo Genera iu suas
same effect Hoff bauer, Uber die Ana- Formas." " Contra communem sen-
hjsis in der Philosophic, p. 41 et sum et verborum naturam, Syntheti-
seq., Halle, 1810. Gassendi, Pliy- cam vocant Methodum, qufe dividit,
sica, Sectio iii. Memb. Part, L. ix. Analyticam contra, qua3 componit."
Opera, t. ii. p. 460. Victorin, Neue Prasf. sub. fin. Iu the edition of the
natilrlichere Darstellung der Logik, § Prcecepda by Maa,ss, Wyttenbach is
214. Trendelenburg, £'fc;)ien to Zocy/ces made to say precisely the reverse of
AristotcUrce, p. 89. Troxler, Logik, ii. what he lays down in the original
p. 100, n.**. Krug,Zo(ifJi, §114, p. 406, edition. — See Prcec. Phil. Log., ed.
u. **, and § 120, p. 431. Wyttenbach Maass, p. 64.— Ed.]
makes Synthetic method progress from
LECTURES ON LOGIC.
LECT.
XXIV.
with cadi
other.
Hence the
terms An-
alysis and
Synthesis
used in a
contrary
sense.
that what in the one is a part is necessarily in the
other a whole. It is evident, then, that the counter
processes of Analysis and Synthesis, as applied to these
counter wholes and parts, should fall into one or cor-
respond ; inasmuch as each in the one quantity should
be diametrically opposite to itself in the other. Thus
Analysis, as applied to Comprehension, is the reverse
process of Analysis as applied to Extension, hut a
corresponding process with Synthesis ; and vice versa.
Now, should it happen that the existence and opposi-
tion of the two quantities are not considered, — that
men, viewing the whole of Extension or the whole of
Comprehension, each to the exclusion of the other,
must define Analysis and Synthesis with reference
to that single quantity which they exclusively take
into account ; — on this supposition, I say, it is mani-
fest that, if different philosophers regard different
wholes or quantities, we may have the terms analysis
and synthesis absolutely used by different philosophers
in a contrary or reverse sense. And this has actually
happened. The ancients, in general, looking alone to
the whole of Extension, use the terms analysts and
analytic simply to denote a division of the genus into
species, — of the species into individuals ; the moderns,
on the other hand, in general, looking only at the
whole of Comprehension, employ these terms to express
a resolution of the individual into its various attri-
butes.** But though the contrast in this respect
between the ancients and moderns holds in general,
still it is exposed to sundry exceptions ; for, in both
periods, there are philosophers found at the same game
of cross-purposes with their contemporaries as the
a [See Aristotle, Physica, L. iv. c. i. qu. 1], p. 248.]
3. Timpler, Lo<jka; Systema, L. ii. c.
LECTURES ON LOGIC. 7
ancients and moderns in 2:eneral are with each other, lect.
XXIV
This difference, which has never, as far as I know, been — '-
fully observed and stated, is the cause of great con-
fusion and mistake. It is proper, therefore, when we
use these terms, to use them not in exclusive relation
to one whole more than to another ; and at the same
time to take care that we guard against the misappre-
hension that might arise from the vague and one-sided
view which is now universally prevalent. So much
for the meaning of the words analytic and synthetic,
which, by the way, I may notice, are, like most of our
logical terms, taken from Geometry."
The Synthetic Method is likewise called the Pro- The Synthe-
gressive ; the Analytic is called the Regressive. Now has beeu
it is plain that this application of the ievms j^rogressive Progressive,
. . . aud the An-
and 'regressive is aJtogether arbitrary, i^ or the import aiytic the
„ . , , . " . . Regressive.
01 these words expresses a relation to a certain point These desig-
of departure, — a terminus a quo, and to a certain point "hoir/arii-
of termination, — a terminus ad quern ; and if these o^vlrious
have only an arbitrary existence, the correlative words "^"^^ '^'''^'""'
will, consequently, only be of an arbitrary application.
But it is manifest that the point of departure, — the
point from which the Progressive process starts, — may
be either the concrete realities of our experience, — the
2:>rincipiata, — the notiora nobis; or the abstract gen-
eralities of intelligence, — the lyrincipia, — the notiora
natura. Each of these has an equal right to be re-
garded as the starting-point. The Analytic process is
chronologically first in the order of knowledge, and
we may, therefore, reasonably call it the i:)rogressive,
as starting from the primary data of our observation.
a See above, vol. i. p. 279, n. ;8. — Philoponus, In An. Post., f. 36*
Ed. [On theAnalj'sis of Geometry, see Veuet. 1534.]
Plotinus, Ennead., iv. L. ix. c. 5.
LECTURES ON LOGIC.
LECT.
XXIV.
In general,
Syutliosis
has been
designated
tiie Progres
sive, and
Analysis
the Regres-
sive Pro-
cess.
Method in
sjiecial.
Oil the other hand the Synthetic process, as following
the order of constitution, is first in the order of nature,
and we may, therefore, likewise reasonably call it the
2)rogressive, as starting from the primary elements of
existence. The application of these terms as syno-
nyms of the analytic and synthetic processes, is, as
wholly arbitrary, manifestly open to confusion and
contradiction. And such has been the case. I find
that the philosophers are as much at cross-purposes in
their application of these terms to the Analytic and
Synthetic processes, as in the application of analysis
and synthesis to the different wholes.
In general, however, both in ancient and modern
times, Synthesis has been called the Progressive,
Analysis the Regressive, process ; an application of
terms which has probably taken its rise from a pas-
sage in Aristotle, who says, that there are two ways
of scientific procedure, — the one from principles (0,770
T(ov ap^(xiv), the other to principles, (eVt ra? ap\a<^.)
From this and from another similar passage in
Plato (?) the term pi'ogressive has been applied to the
process of Comprehensive Synthesis, [progrediendi a
2orincipiis ad jjrincipiata), the term regressive, to the
process of Comprehensive Analysis, (lyrogrediendi a
pinncipiatis ad principia.) "
So much for the general relations of Method to
thought, and the general constituents of Method itself
It now remains to consider what are the particular
a Eth. Nic, i. 2 (4). The reference
to Plato, whom Aristotle mentions as
making a similar distinction, is pro-
bably to be fouii% \y^ comparing two
separate passages- irf'' the Republic, B.
iv. p. 435, vi. p. 504. — Ed. [Plato is
said to have taught Analysis to Leoda-
mas the Thasian. See Laertius, L. iii.
24, and Proclus, quoted in Is. Casau-
bon's note. On the views of Method of
Aristotle and Plato, see Scheibler and
Dowuam.] [Scheibler, Opera Logica,
Pars iv., Tract. Si/llog., c. xviii., De
Methodo, tit. 7, p. 603. Downam, Co7n.
in P. Rami Dialecticam, L. ii. c. 1 7, p.
482.— Ed.]
LECTUE-ES ON LOGIC. 9
applications of Method, by wliich Logic accomplishes lect.
the Formal Perfection of thought. In doing this, it is — - — 1-
evident that, if the formal perfection of thought is
made up of various virtues, Logic must accommodate
its method to the acquisition of these in detail ; and
that the various processes by which these several
virtues are acquired, will in their union constitute the
system of Logical Methodology. On this I will give
you a paragraph.
H LXXXL The Formal Perfection of thought Par. lxxxi.
is made up of the three virtues or characters : — MeUiod-
1°, Of Clearness; 2°, Of Distinctness, involving Three' Parts.
Completeness; and, 3°, Of Hannonij. The char-
acter of Clearness depends principally on the de-
termination of the Comprehension of our notions;
the character of Distinctness depends principally
on the development of the Extension of our
notions ; and the character of Harmony, on the
mutual Concatenation of our notions. The rules
by which these three conditions are fulfilled, con-
stitute the Three Parts of Logical Methodology.
Of these, the first constitutes the Doctrine of
Dejinition; the second, the Doctrine of Division;
and the third, the Doctrine of Probation. °'
a Kriig, Loi/ik, § 121". — Ed. [Ra- mascus speaks strongly of Method in
mus was the first to inti'oduce Method his Dialectic, ch. G8, and makes four spe-
as a part of Logic under Syllogistic, cial logical methods, Division, Defini-
(see his Dialectica, L. ii. c. 17), and tion, Analysis, Demonstration. Eusta-
the Poi't Royalists, (1662), made it a chius treats of Method under Judg-
f ourth part of logic. See La Lor/ique ment, and Scheibler under Syllogistic]
ou L'Art dc Pcnser, Prem. Dis., i>. 26, [Eustachius, Summa Pliilosophice, Lo-
pp. 47, 50. Quat. Part., p. 445 et seq. gica, P. ii. Tract. 2. De Methodo, p.
ed. 1775. Gassendi, in his Institutio 106, ed. Lugd. Batav., 1747. First
Logica, has Pars iv., De Methcdo. edition, 1609. Scheibler, 0/Je»'a i or/ j-
He died in 1655 ; his Logic appeared ca, Pars iv. c. xviii. p. 69o et seq. —
posthumously in 1658. John of Da- Ed.]
10 LECTURES ON LOGIC.
LECT. "When we turn attention on our tbouo-lits, and
XXIV
(leal with them to the end that they may be consti-
don ^'"'^ tuted into a scientific whole, we must perform a three-
fold operation. We must, first of all, consider what
we think, that is, what is comprehended in a thought.
In the second place, we must consider how many
things we think of, that is, to how many objects the
thought extends or reaches, that is, how many are
conceived under it. In the third place, we must con-
sider why we think so and so, and not in any other
manner ; in other words, how the thoughts are bound
together as reasons and consequents. The first con-
sideration, therefore, regards the comprehension ; the
second, the extension ; the third, the concatenation of
our thoughts. But the comprehension is ascertained
by definitions ; the extension by divisions ; and the
concatenation by probations." " We proceed, therefore,
to consider these Three Parts of Lomcal Methodoloo;v
in detail ; and first, of Declaration or Definition, in
regard to which I give the following paragraph.
Par. Lxxxii. ^ LXXXII. How to make a notion Clear, is
trine'of De- showu by thc logical doctrine of Declaration, or
and Defini- Definition in its wider sense. A Declaration, (or
Definition in its wider sense), is a Categorical
Proposition, consisting of two clauses or members,
viz. of a Subject Defined, {memhrum definitum),
and of the Defining Attributes of the subject, that
is, those by which it is distinguished from other
things, {rnemhrutn dejinieus). This latter mem-
ber really contains the Definition, and is often
itself so denominated. Simple notions, as con-
a Krug, Logilc, § 121'''. — Ed.
LECTURES ON LOGIC. 11
taining no plurality of attributes, are incapable lect.
of definition." 1
The terms declaration and dejinition, which are here Expiica-
used as applicable to the same process, express it, xiie terms
however, in different aspects. The term declaration , and Defini-
(declaratio), is a word somewhat vaguely employed inthTsamJ^^*
English ; it is here used strictly in its proper sense a^fferenr
of throwing light upo7i, — clearing up. The term defini- ^^^"^ ^'
tion, (definitio), is employed in a more general, and in
a more special, signification. Of the latter we are soon
to speak. At present, it is used simply in the meaning
of an enclosi7ig ivithin limits, — the separating a thing
from others. AVere the term declaration not of so vague
and vacillating a sense, it would be better to employ it
alone in the more general acceptation, and to reserve
the term dejinition for the special signification.
T LXXXIII. The process of Definition is Par.Lxxxin.
,-,.■,,. f»ri T • Definition
founded on the logical relations oi Subordination, in its stricter
sense, —
Co-ordination, and Congruence. To this end we what,
discriminate the constituent characters of a no-
tion into the Essential, or those which belong to
it in its unrestricted universality, and into the
Unessential, or those which belong to some only
of its species. The Essential are again discrim-
inated into Original and Derivative, a division
which coincides with that into Internal or Pro-
per, and External. In giving the sum of the
original characters constituent of a notion, con-
sists its Definition in the stricter sense. A De-
finition in the stricter sense must consequently
a Ki-ug, Lwjik, § 121b.— Ed.
12 LECTURES ON LOGIC.
LECT. afford at least two, and properly only two, ori-
-I-1_J- pinal characters, viz. that of the Genus imme-
diately superior, {genus iwoximum), and that of
the Difference by which it is itself marked out
from its co-ordinates as a distinct species, {iiota
specialis, differentia specifica) «
Expiica- Declarations (or definitions in the wider sense), ob-
Various talu various denominations, according as the process
Declaration, is performed in different manners and degrees. A
Expiica- Declaration is called an Explication, (explicatio), when
the predicate or defining member indeterminately
evolves only some of the characters belonging to the
Exposition, subject. It is called nji Exposition, {expositio), when
the evolution of a notion is continued through several
Description. expHcatious. It is called a Description, [descriptio),
when the subject is made known through a number of
Definition coucretc characteristics. Finally, it is called a Defi-
nition Proper, when, as I have said, two of the essen-
tial and original attributes of the defined subject are
given, whereof the one is common to it with the
various species of the same genus, and the other dis-
criminates it from these.^
Definitions, " Defiuitlous arc distinguished also into Verbal or
Reai°"ud ' Nominal, into Eeal, and into Genetic, [definitiones no-
minales, reales, geneticce), according as they are con-
versant with the meaning of a term, with the nature
of a thing, or with its rise or production.''' Nominal
Definitions are, it is evident, merely explications.
They are, therefore, in general only used as prelim-
inary, in order to prepare the way for more perfect
a [Cf. Arif3totle, Topka, i. 6. Keck- Logik, p. 94.]
ermaun, Si/stema Logicce Minus, L. i. j8 Cf. Krug, Logil; § 122. — Ed.
c. 17. Opera, t. i. pp. 199, 656. y [Cf. Eeusch, Systema Loglcum, §
Scheibler, To2nca, c. 30. Richter, 309 et scq.]
LECTURES ON LOGIC. 13
declarations. In Eeal Definitions the thing defined is lect.
considered as already there, as existing (ov), and the .U 1
notion, therefore, as given, precedes the definition.
They are thus merely analytic, that is, nothing is
given explicitly in the predicate or defining member,
which is not contained implicitly in the subject or
member defined. In Genetic Definitions the defined
subject is considered as in the progress to be, as be-
coming iyiyvoixevov) ; the notion, therefore, has to be
made, and is the result of the definition, which is con-
sequently synthetic, that is, places in the predicate or
defining member more than is given in the subject or
member defined. As examples of these three species,
the following three definitions of a circle may suffice : —
1. The Nominal Definition, — The word circle signifies
an uniformly curved line. 2. The Real Definition, —
A circle is a line returning upon itself, of which all
the parts are equidistant from a given point. 3. The
Genetic Definition, — A circle is formed when we draw
around, and always at the same distance from, a fixed
point, a movable point w^hich leaves its trace, until
the termination of the movement coincides with the
commencement.* It is to be observed that only those
notions can be genetically defined, which relate to
quantities represented in time and sj^ace. Mathema-
tics are princijDally conversant with such notions, and
it is to be noticed that the mathematician usually de-
nominates such genetic definitions real definitions,
while the others he calls without distinction nominal
definitions!' ^
The laws of Definition are given in the following
paragraph.
a This example is taken, with some ;8 Krug, Zo'///,-, § 122. Aniii. 3, pp.
alteration, from Wolf, PhUosojihia 448, 449. — Ed.
ItatlonaVis, % 191.— Ed.
14 LECTURES ON LOGIC.
LECT. T LXXXIV. A definition should be Adequate
— L (adequata), that is, the subject defined, and the
Par. LXXXIV, predicate defining, should be equivalent or of the
Definition, . _„ - . _ ., ^.
—its Laws. same extension, it not, the sphere oi the predi-
cate is either less than that of the subject, and
the definition Too Narrow, {angustior), or greater,
and the definition Too Wide (latior).
II. It should not define by Negative or Divi-
sive attributes, {Ne sit negaus, ne flat j9er dis-
juncta).
III. It should not be Tautological, — what is
contained in the defined, should not be repeated
in tlie defining clause, {Ne sit circvlus vel dicdlelon
m definiendo).
IV. It should be Precise, that is, contain no-
thing unessential, nothing suj^erfluous, {Definitio
ne sit abundans).
V. It should be Perspicuous, that is, couched
in terms intelligible, and not figurative, but
proper and compendious."
Expiica- The First of these rules : — That the definition should
tiou.
First Rule, bc adcquatc, that is, that the dcfinieiis and definitum
should be of the same extension, is too manifest to
require much commentary. Is the definition too
wide"? — then more is declared than ouoht to be
declared ; is it too narrow '? — then less is declared
than ought to be declared ; — and, in either case, the
definition does not fully accomplish the end which it
proposes. To avoid this defect in definition, we must
attend to two conditions. In the first place, that
a Of. Kvug, Logih, § 123. — Ed. nitione, Oxiera,^^. Qi?> et xeq. Buffier,
[Victorin, Logik, § 223 ct seq. Sig- Veritez de Consequence, %i5-51. Gocle-
wart, JIandbut'h zu, Vorlemngen ilber nius, Lexicon, Philosophiciim, v. Defin-
die Lotjik, § 371. Boethius, De Defi- itio, p. 500.]
LECTURES ON LOGIC. 15
.ittribute should be given which the thinsr defined lect.
. XXIV
has in common with others of the same class ; and, in '-
the second j^lace, that attribute should be given which
not only distinguishes it in general from all other
things, but proximately from things which are in-
cluded with it under a common class. This is ex-
23ressed by Logicians in the rule — Definitio constet
genere 2^^'oximo et diferentia ultima, — Let the defin-
ition consist of the nearest genus and of the lowest
difference. But as the notion and its definition, if this
rule be obeyed, are necessarily identical or convertible
notions, they must necessarily have the same extent ;
consequently, everything to which the definition ap-
plies, and nothing to which it does not apply, is the
thing defined. Thus ; — if the definition, Man is a
rational animal, be adequate, we shall be able to say
— Every rational animal is human : — nothing ichich
is not a rational animal is human. But we cannot say
this, for though this may be true of this earth, we can
conceive in other worlds rational animals which are
not human. The definition is, therefore, in this case
too wide ; to make it adequate, it will be necessary to
add terrestrial or some such term — as, Man is a ra-
tional animal of this earth. Again, were we to define
Man, — a rationally acting animal of this earth, — the
definition would be too narrow ; for it would be false
to say, no animal of this earth not acting rationally is
human, for not only children, but many adult persons,
would be excluded by this definition, which is, there-
fore, too narrow."
The Second Rule is, — That the definition should not second
be made by negations, or disjunctions. In regard to
the former, — negations, — that we should define a thing
a Cf. Krug, Lotj'tl-, % 123. Aiini. i.^Ec
iscTTSE? OS tiwac
XXTf
i>f it.
nvgi.^
X3Er;Z3:H2=
IZ'ITTEES OS UjGIC. 17
to assnie ns. Bnt a de£il:i'-- by dUpaiaze aixecL^- lect.
lives is, thongh. it mav Taz^e^r circnmsciibe a no^icaii, 1
only to Ve 'Musiiered as a prelii=':»ry deirnTtJoiL and
as ihr _ LT and yet inipQ^ecx knov-
led^. >'» r most not. no^'eTer, confoon^. dc^DiticHis
by 'iivisive arrritz.'.-is -sitb propoeitioiis eipre^ve of
a divisioii.
TLeTl:: :._r is-— T-- _ . .
tantologicai ; tiiat is.
defined by itseli Ti-is tic'z ir -j De^bea
Circle. This mlf ' ~ r - .-*
or mediately. T.^ -
memd, — ^is an ex;:.!- - : - Ar^^
diate cirde requires, at least, xwa
itioDS, a pdndpsd smd a safaEadiazy. i —
Lair is the expressed iris4 <^' a ruler,
one tcho estabGghes laits. Tbe drde.
diate or mediate, is manifest or o: _
the things defined is reiieated in tl
^i-ith other synonynioos vordr
example it was manifest- In tl : _
cealed : — Gratitude is a nrtue —
BigJit is Ae competence to do or hid to do. Sodi
dedaiations may. however, be aDoved t
lusoiy or ncHninal definitions^ Ccaiceal^
finitions are of very ^- "fnt ocerarez-- ___ :__
aie at iiie same tim; :? ox remote : for we «rr
very apt to aUoir ourselves to l:«e deceived by :L
ferenee of explosion, and &ncy that we
a notion when we have oiii~ ~r t . p — ^-
We ought, therefoxe, to l«r -- _ ^5 izsirst
this besetting vice. TL:
definition also by tl : i :l5 iz uiis
case we declaie the *i<ii
VOL II. z
18 LECTURES ON LOGIC.
LECT. procally by each otlier (St' dWajXcovy. In probation
'- there is a similar vice which bears the same names."^
We may, I think, call them by the homely English
appellation of the Seesatv. —
Fourth The Fourth Rule is, — " That the definition should be
precise ; that is, contain nothing unessential, nothing
superfluous. Unessential or contingent attributes are
not sufficiently characteristic, and as they are now
present, now absent, and may likewise be met with in
other things which are not comprehended under the
notion to be defined, they, consequently, if admitted
into a definition, render it sometimes too wide, some-
times too narrow. The well-known Platonic defini-
tion, — ' Man is a two-legged animal without feathers,'
■ — could, as containing only unessential characters, be
easily refuted, as was done by a plucked cock.'^ And
when a definition is not wholly made up of such attri-
butes, and when, in consequence of their intermixture
with essential characters, the definition does not abso-
lutely fail, still there is a sin committed against logical
purity or precision, in assuming into the declaration
qualities such as do not determinately designate what
is defined. On the same principle, all derivative cha-
racters ought to be excluded from the definition ; for
although they may necessarily belong to the thing
defined, still they overlay the declaration with super-
fluous accessories, inasmuch as such characters do not
designate the original essence of the thing, but are a
mere consequence thereof. This fault is committed in
the following definition : — The Circle is a curved line
returning upon itself, thej^arts ofivhich are at an equal
a Compare SextusEmpiricus,P^V'')'/(. ^ Krug, Logik, § 123. Anm. 3. —
//y/:i., i. 169, ii. C8.— Ed. " Ed.
7 Diog. Laert., \'i. 40. — Ed.
LECTURES ON LOGIC. 19
distance from the central point. Here precision is vio- lect,
lated, though the definition be otherwise correct. For — '-
that every line returning upon itself is curved, and
that the point from which all the parts of the line are
equidistant is the central point, — these are mere con-
sequences of the returning on itself, and of the equi-
distance. Derivative characters are thus mixed up
with the original, and the definition, therefore, is not
precise." '^
The Fifth Kule is, — " That the definition should be Fifth Rule,
perspicuous, that is, couched in terms intelligible, not
figurative, and compendious. That definitions ought
to be perspicuous, is self-evident. For why do we de-
clare or define at all 1 The perspicuity of the defini- in order to
1 -\ • ^ n 1 i'iT-11 perspicuity
tion depends, m the first place, on the intellio;ible in Defini-
1 PIT 11- -1 ? tion, 1. The
character oi the language, and this again depends on language
the employment of words in their received or ordinary intelligible.
signification. The meaning of words, both separate
and in conjunction, is already determined by conven-
tional usage ; when, therefore, we hear or read these^
we naturally associate with them their ordinary mean-
ing. Misconceptions of every kind must, therefore,
arise from a deviation from the accustomed usage ;
and though the definition, in the sense of the definer,
may be correct, still false conceptions are almost in-
evitable for others. If such a deviation becomes neces-
sary, in consequence of the common meaning attached
to certain words not corresponding to certain notions,
there ought at least to be appended a comment or
nominal definition, by which we shall be warned that
such words are used in an acceptation wider or more
restricted than they obtain in ordinary usage. But, in
o Krug, Locjil; § 123. Anm. 2.— Ed.
20 LECTURES ON LOGIC.
LECT. the second place, words ought not only to be used in
^^^^' their usual signification, — that signification, if the de-
melning finitiou bo perspicuous, must not be figurative but
must be not pj-Qpgp^ Tropcs aud figures are logical hieroglyphics,
meaning
must be E
figurative
but proper. ^^^ thcmselves require a declaration. They do not
indicate the thing itself, but only something similar.""
Such, for example, are the definitions we have of Lo-
gic as the Pharus Intellectus, — the Lighthouse of the
Understanding, — the Cynosura Veritatis, — the Cpio-
sure of Truth, — the Medicina Mentis, — the Physic of
the Mind, &c.^
" However, many expressions, originally metapho-
rical, (such as conception, imagination, comprehension,
representation, kc. &c.), have by usage been long since
reduced from figurative to proper terms, so that we
may em^^loy these in definitions without scruple, —
nay frequently must, as there are no others to be
found.
3 The defi- " jj^ ^l^g third place, the perspicuity of a definition
mtion must ■•• ■•• J- -^
be brief, depends upon its brevity. A long definition is not
only burthensome to the memory, but likewise to the
understanding, which ought to comprehend it at a
single jet. Brevity ought not, however, to be pur-
chased at the expense of perspicuity or completeness."'''
The other " Thc rulcs hithcrto considered, proximatelv relate to
kinds of T^£•• • ^ • r ^
Declaration. Deilmtions ID. the strictcr sense. In reference to the
other kinds of Declaration, there are certain modifica-
Diiucida- tions and exceptions admitted. These Dilucidations
tions or Ex- .
plications, or Jlixplications, as they make no pretence to logical
perfection, and are only subsidiary to the discovery of
more perfect definitions, are not to be very rigidly
dealt with. They are useful, provided they contain
a Krug, Logik, § 123. Anm. 4.— & See above, vol. i. y>- 3.5.— Ed.
Ed. 7 Krug, tVj/f/.— Ed.
LECTURES ON LOGIC. 21
even a sinoile time character, by which we are con- lect.
^ ' -^ XXIV.
ducted to the apprehension of others. They may,
therefore, be sometimes too wide, sometimes too nar-
row. A contingent and derivative character may be
also useful for the discovery of the essential and ori-
ginal. Even Circular Definitions are not here abso- circular
~ _ . Definitions.
lately to be condemned, if thereby the language is
rendered simpler and clearer. Figiu-ative Expressions Figurative
are likewise in them less faulty than in definitions sions.
proper, inasmuch as such expressions, by the analogies
they suggest, contribute always something to the illus-
tration of the notion.
" In regard to Descriptions, these must be adequate, Descrip-
and no circle is permitted in them. But they need
not be so precise as to admit of no derivative or con-
tingent characters. For descriptions ought to enume-
rate the characters of a thing as fully as possible ; and,
consequently, they cannot be so brief as definitions.
They cannot, however, exceed a certain measure in
point of length.""
o Ki-ug, Lorjih, § 123. Anm. 5. — Eu.
22 LECTURES ON LOGIC.
LECTURE XXV.
METHODOLOGY.
SECTION II. — LOGICAL METHODOLOGY.
II. — DOCTRINE OF DIVISION.
LECT. I NOW proceed to tlie Second Chapter of Logical
Division.
Methodology, — the Doctrine of Division, — the doctrine
which affords us the rules of that branch of Method,
by which we render our knowledge more distinct and
exhaustive. I shall preface the subject of Logical
Division by some observations on Division in general.
Division in " Under Division (cUvisio, Statpecrts) we understand
general. . . ^ . .
in general the sundering of a whole into its parts.*
The object which is divided is called the divided whole
{totum divisum), and this whole must be a connected
many, — a connected multiplicity, for otherwise no
division would be possible. The divided whole must
comprise at least one character, affording the condition
of a certain possible splitting of the object, or through
which a certain opposition of the object becomes
recognised ; and this character must be an essential
attribute of the object, if the division be not aimless
and without utility. This point of view, from which
alone the division is possible, is called the principle of
the division {principiimi sive fundamentum divisi-
a [On Division and its various kinds, f. 6^, Aid. 1546.]
see Ammonias, Be Qiiinque Vocibus,
LECTURES ON LOGIC. 23
onis) ; and the parts which, by the distraction of the lect.
whole, come into view, are called the divisive memhers — — 1-
{membra dividentia). When a whole is divided into
its parts, these parts may, either all or some, be them-
selves still connected multiplicities ; and if these are
again divided, there results a subdivision {suhdivisio),
the several parts of which are called the suhdivisive
7ne7nhers {me^nhi^a suhdividentia). One and the same
object may, likewise, be differently divided from dif-
ferent points of view, whereby condivisions {condivisi-
ones) arise, which, taken together, are all reciprocally
co-ordinated. If a division has only two members, it is
called a dichotomy {dichotomia) ; if three, a trichotomy
(trichotomia) ; if four, a tetrachotomy ; if many, a
2^olytomy, &c.
" Division, as a genus, is divided into two species. Division of
according to the different kind of whole which it sun- -^PaTikTon
ders into parts." These parts are either contained in Divisir
the divided whole, or they are contained under it. In
the former case the division is called a, 2^ci)tition {par-
titio, a7rapWix7)(rii),^ in the latter, it is named a logical
division? Partition finds an application only when
the object to be divided is a whole compounded of
parts, — consequently, where the notion of the object
is a complex one ; Logical Division, on the other hand,
finds its application only where the notion contains a
plurality of characters under it, and where, conse-
quently, the notion is an universal one. The simple
a [On various kinds of Wholes, see a subject into successive heads, first,
Caramuel, Jiationalis et Realis Philo- second, &c. See Hermogenes, Ilepl
sojohia, L. iv. sect. iii. disp. iv. p. 277,] iSecav. Rhetores Grceci, i. p. 104, ed.
[and above. Lectures on M elaphysics, Aid. — Ed.
vol. ii. p. 340 ; Lectures onLor/ic, vol. i. y [See Keckermaian, SystemaLogicce,
p. 201 Ed.] L. i. c. 3. Opera, t. i. p. 667. Dro-
^'Airapieixria-is is properly a rhetori- bisch, ^^eue Darstellunfj der Logik,%
cal term, and signifies the division of 112. Krug, Logik, § 124. Anm. 2.]
24 LECTURES ON LOGIC.
LECT. notion is thus the limit of Partition ; and the indi-
'^'^^' vidual or singuLar is thus the limit of Division. Par-
Partition titlou is divldcd into a physical or real, when the
either Real j. i/
or Ideal, parts can actually be separated from each other ; and
into a metaphysical or ideal, when the parts can only
be sundered by Abstraction." It may be applied in
order to attain to a clear knowledge of the whole, or
to a clear knowledge of the parts. In the former case,
the parts are given and the whole is sought ; in the
latter, the whole is given and the parts are sought.
If the whole be given and the parts sought out, the
object is first of all separated into its proximate, and,
thereafter, into its remoter parts, until either any
further partition is impossible, or the partition has
attained its end. To this there is, however, required
an accurate knowledge of the object, of its parts proxi-
mate and remote, and of the connection of these parts
together, as constituting the whole. We must, like-
wise, take heed whether the partition be not deter-
mined from some particular point of view, in conse-
quence of which the notions of more proximate and
more remote may be very vague and undetermined.
a By Partition, triangle maj' be dis- celes, and scalene. (The dichotomic
tiuguished, 1 °, Into a certain portion division would, however, be here more
'of space included within certain bound- proper.) By i-eference to the angles,
aries ; 2°, Into sides and angles ; 3°, they are divided into the three species
Into two triangles, or into a trapezium of rectangular, i.e. triangle which has
and a triangle. The first two pai'ti- one of its angles right ; into ambly-
tions are ideal, they cannot be actually gon, or ti'iangle which has one of its
accomplished. The last is real, it may. angles obtuse; and into oxygon, /. c.
By Division, triangle is distinguish- triangle which has its three angles
ed, 1°, Into the two species of recti- acute.
linear and curvilinear. 2°, Both of By Definition, triangle is distiu-
these are again subdivided (A) by guished into figure of three sides,
reference to the sides, (B) by refer- equal to triangular figure ; that is,
euce to the angles. By reference to into figure, the proximate genus, and
the sides, triangles are divided into trilateral or three-sided, the differen-
the three species of equilateral, isos- iial quality.
LECTURES ON LOGIC. 25
If the parts be given, and from them the whole sought lect.
out, this is accomplished when we have discovered the —
order, — the arrangement, of the parts ; and this again
is discovered when the principle of division is dis-
covered ; and of this we must obtain a knowledge,
either from the general nature of the thing, or from
the particular end we have in view. If, for example,
a multitude of books of every various kind are arranged
into the whole of a weU-ordered library ; — in this case
the greater or lesser similarity of subject will afford,
either exclusively or mainly, the principle of division.
It happens, however, not unfrequently, that the parts
are ordered or arranged according to different rules,
and by them connected into a whole ; and, in this
case, as the different rules of the arrangement
cannot together and at once accomplish this, it is
proper that the less important arrangement should
yield to the more important ; as, for example, in the
ordering of a library, when, besides the contents of
the books, we take into account their language, size,
antiquity, binding, &C.'"'
I now proceed to Logical Division, on which I give
you the following paragraph : — •
H LXXXV. The Distinctness and Completeness Par. lxxxv,
of our knowledge is obtained by that logical pro- DiSn.
cess which is termed Division (divisio, Statpeo-t?).
Division supposes the knowledge of the w'hole to
be given through a foregone process of Definition
or Declaration ; and proposes to discover the
parts of this whole which are found and deter-
mined not by the development of the Comprehen-
sion, but by the development of the Extension.
a Esser, Logik, §§ 134, 135, p. 2G1-64.— Eu.
2G LECTURES ON LOGIC.
i-ECT. As Logical Definition, therefore, proposes to ren-
— ^- — — der the cliaracters contained in an object, that
is, the comprehension of a reality or notion,
Clear ; Logical Division proposes to render the
characters contained under an object, that is, the
extension of a notion. Distinct and Exhaustive.
Division is, therefore, the evolution of the exten-
sion of a notion ; and it is expressed in a dis-
junctive proposition, of which the notion divided
constitutes the subject, and the notions contained
under it, the predicate. It is, therefore, regu-
lated by the law which governs Disjunctive
Judgments, (the Principle of Excluded Middle),
although it is usually expressed in the form of a
Copulative Categorical Judgment. The rules by
which this process is regulated are seven : —
1°. Every Division should be governed by
some principle, (Divisio ne caveat fundamento).
2°. Every Division should be governed by only
a single principle,
3°. The principle of Division should be an
actual and essential character of the divided
notion, and the division, therefore, neither com-
plex nor without a purpose.
4°. No dividing member of the predicate must
by itself exhaust the subject.
5°. The dividing members, taken together,
must exhaust, but only exhaust, the subject.
6°. The divisive members must be reciprocally
exclusive.
7°. The divisions must proceed continuously
from immediate to mediate differences, {Divisio
nejiat 2^er saltum).
LECTURES ON LOGIC. 27
In tliis paragraph are contained, first, the general lect,
XXV.
Principles of Logical Division, and, secondly, the Laws
by which it is governed. I shall now illustrate these tiou. ""^
in detail.
In the first place, it is stated that " the distinct-
ness and completeness of our knowledge is obtained
by that logical process which is termed Division
[divisio, Statpeo-t?). Division supposes the know-
ledge of the whole to be given through a foregone
process of definition, and proposes to discover the
parts of this whole which are found and determined
not by the development of the comprehension, but
by the development of the extension. As logical
definition, therefore, proposes to render the characters
contained in a notion, that is, its comprehension, clear;
logical division proposes to render the characters con-
tained under an object, that is, the extension of a
notioD, distinct. Division is, therefore, the evolution
of the extension of a notion, and it is expressed in a
disjunctive proposition, of which the notion divided
constitutes the subject, and the notions contained
under it, the predicate. It is, therefore, regulated by
the law which governs disjunctive judgments (the
principle of excluded middle), although it be usually
expressed in the form of a copulative categorical
judgment."
The special virtue, — the particular element, of per- Endof Divi-
. . . . sion is Dis-
fect thmkmo', which Division enables us to acquire, tinctness,
-P^ 1 • • • • 1 i which in-
is Distinctness, but, at the same time, it is evident vohes
. T 1 1 • • 1 1 • Complete-
that it cannot accomplish this without rendering ness.
our thinking more complete. This, however, is only
a secondary and collateral result ; for the problem
which division proximately and principally proposes
28 LECTURES ON LOGIC.
LECT. to solve is, — to afford us a distinct consciousness of
L the extension of a given notion, tlirough a complete
or exhaustive series of subordinate or co-ordinate
notions. This utility of Division, in rendering our
knowledge more complete, is, I find, stated by Aris-
totle,'' though it has been overlooked by subsequent
logicians. He observes that it is only by a regular
division that we can be assured, that nothing has been
omitted in the definition of a thing.
As many " As it Is by mcaus of division that we discover
Division what are the characters contained under the notion of
there are au objcct, it follows that there must be as many kinds
affording a of divislou posslblc as there are characters contained
Division, under the notion of an object, wdiich may afibrd the
principle of a different division. If the characters
which aff'ord the principle of a division are only ex-
ternal and contingent, there is a division in the wider
sense ; if, again, they are internal and constant, there
is a division in the stricter sense ; if, finally, they are
not only internal but also essential and original, there
A universal is a dlvlsiou ID. tlic strictcst scusc. From the very
notion tlie . „,.,-,... . .
only object conceptiou of lo^ical division, it is manifest that it
of Logical ^ 1- 1 1 •
Division, can only be applied where the object to be divided is
a universal notion, and that it is wholly inapplicable
to an individual ; for as the individual contains no-
thing under it, consequently it is not susceptible of
General ail ultcrior divlsiou. The efeneral problem of which
problem of . . , ox
Division, division affords the solution is, — To find the subor-
dinate genera and species, the higher or generic notion
being given. The higher notion is always something
abstracted, — something generalised from the lower
notions, with which it agrees, inasmuch as it contains
all that is common to these inferior concepts, and from
a Anal. Post., L. ii. c. 13.
LECTURES ON LOGIC. 29
which it differs, inasmuch as they contain a greater lect.
number of determinino' characters. There thus sub-
sists an internal connection between the higher and
the lower concepts, and there is thus afforded a tran-
sition from the superior notion to the subordinate,
and, consequently, an evolution of the lower notions
from the higher. In order to discover the inferior
genera and species, we have only to discover those
characters which afford the proximate determinations,
by which the sphere or extension of the higher notion
is circumscribed. But to find what characters are
wanted for the thorough -going determination of a
higher notion, we must previously know what char-
acters the higher notion actually contains, and this
knowledge is only attainable by an analysis, — a sund-
ering of the higher notion itself. In doing this, the
several characters must be separately drawn forth and
considered ; and in regard to each, we must ascertain
how far it must still be left undetermined, and how
far it is capable of opposite determinations. But
whether a character be still undetermined, and of
what opposite determinations it is capable, — on these
points it is impossible to decide a priori, but only
a ])osteriori, through a knowledge of this particular
character and its relations to other notions. And the
accomplishment of this is rendered easier by two
circumstances ; — the one, that the generic notion is
never altogether abstract, but always realised and held
fast by some concrete form of imagination ; — the
other, that, in general, we are more or less acquainted
with a greater or a smaller number of special notions,
in which the generic notion is comprehended, and
these are able to lead us either mediately or imme-
diately to other subordinate concepts.
,30 LECTURES ON LOGIC.
LECT. " But tlie determinations or constituent cliaracters
. L of a notion which we seek out, must not only be com-
pletely, but also precisely, opposed. Completely, in-
asmuch as all the species subordinate to the notions
ought to be discovered ; and precisely, inasmuch as
whatever is not actually a subordinate species, ought
to be absolutely excluded from the notion of the
genus.
" In regard to the completeness of the opposition,
it is not, however, required that the notion should
be determined through every possible contradictory
opposition ; for those at least ought to be omitted,
concerning whose existence or non-existence the notion
itself decides. In regard to the opposition itself, it
is not required that the division should be carried
through by contradictory oppositions. The only oppo-
sition necessary is the reciprocal exclusion of the
inferior notions into which the higher notion is
divided." " In a mere logical relation, indeed, as we
know nothing of the nature of a thing more than that
a certain character either does or does not belong to
it, a strictly logical division can only consist of two
contradictory members, for example, — that angles are
either right or not right, — that men are either white
or not white. But looking to the real nature of the
thing known, either a iwiori or a posteyioiH, the divi-
sion may be not only dichotomous but polytomous,
as for example, — angles are right, or acute, or obtuse ;
men are white, or black, or copper-coloured, or olive-
coloured, &c.
Rules of We now come, in the second place, to the rules
Divishra. dictated for Logical Division.
These Rules spring either, 1°, From the Principle of
o E«ser, Logil; § 136 Ed.
LECTURES ON LOGIC. 31
Division : or, 2°, From the Eelations of the Dividing lect.
^ XXV.
Members to the Divided Whole ; or, 3°, From the
Eelations of the several Dividins; Members to each
other ; or, 4°, From the relations of the Divisions to
the Subdivisions.
The first of these heads, — the Principle of Division, Those
— comprehends the three first rules. Of these the l From^the
first is self-evident, — There must be some principle, DivS! °
some reason, for every division ; for otherwise there ^"'^ ^''''^'
would be no division determined, no division carried
into efi'ect.
In regard to the second rule, — That every division Second,
should have only a single principle,' — the propriety of
this is likewise sufficiently apparent. In every divi-
sion we should depart from a definite thought, which
has reference either to the notion as a unity, or to some
single character. On the contrary, if we do not do
this, but carry on the process by difi"erent principles,
the series of notions in which the division is realised,
is not orderly and homogeneous, but heterogeneous
and perplexed.
The third rule, — That the principle of division should Tiiird.
be an actual and essential character of the divided
notion, — is not less manifest. " As the ground of divi-
sion is that w^hich principally regulates the correctness
of the whole process, that is, the completeness and
opposition of the division, — it follow^s that this ground
must be of notoriety and importance, and accommo-
dated to the end for the sake of which the division is
instituted. Those characters of an object are best
adapted for a division, whose owm determinations
exert the greatest influence on the determinations of
other characters, and, consequently, on those of the
notion itself ; but such are manifestly not the external
32 LECTURES ON LOGIC.
LECT. and contino;ent, but tlie internal and essential, cha-
X XV
L racters, and, of these, those have the pre-eminence
through whose determination the greater number of
others are determined, or, what is the same thing,
from which, as fundamental and original attributes,
the greater number of the others are derived. The
choice of character is, however, for the most part, regu-
lated by some particular end ; so that, under certain
circumstances, external and contingent characters may
obtain a preponderant importance. Such ends cannot,
however, be enumerated. The character affording the
principle of division must likewise be capable of being
clearly and definitely brought out ; for unless this be
possible, we can have no distinct consciousness of the
completeness and contrast of the determination of
which it is susceptible. We ought, therefore, always
to select those characters for principles of division,
which are capable of a clear and distinct recogni-
tion.'"'
The second part of the rule, — That the division be
not, therefore, too complex, and without a purpose, — is
a corollary of the first. " In dividing, we may go on
to infinity. For while, as was formerly shown, there
is, in the series of higher and lower notions, no one
which can be conceived as absolutely the low^est ;
so in subdividing, there is no necessary limit to the
process. In like manner, the co-ordinations may be
extended ad infinitum. For it is impossible to exhaust
all the possible relations of notions, and each of these
may be employed as the principle of a new division.
Thus we can divide men by relation to their age, to
their sex, to their colour, to their stature, to their
knowledge, to their riches, to their rank, to their man-
o Esser, Loijik, § 137. — Ed.
LECTURES ON LOGIC. 33
ner of life, to their education, to their costume, &c. &c. lect.
xxv.
It would, however, be ridiculous, and render the divi
sions wholly useless, if we multiplied them in this
fashion without end. We, therefore, intentionally
restrict them, that is, we make them comparatively
limited, inasmuch as we only give them that complete-
ness which is conducive to a certain end. In this
manner divisions become relatively useful, or acquire
the virtue of adaptation. In the selection of a prin-
ciple of division, we must take heed whether it be
fertile and pertinent. A ground of division is fertile,
when it affords a division out of which again other
important consequences may be drawn ; it is pertinent,
when these consequences have a proximate relation to
the end, on account of which we were originally in-
duced to develop the extension of a concept. A prin-
ciple of division may, therefore, be useful with one
intent, and useless with another. Soldiers, for example,
may be conveniently divided into cavalry and infantry,
as this distinction has an important influence on their
determination as soldiers. But in considerino; man in
general and his relations, it would be ludicrous to
divide men into foot and liorsemen ; while, on the
contrary, their division would be here appropriate
according to principles which in the former case would
have been absurd. Seneca" says well, — 'Quicquid in
majus crevit facilius agnoscitur, si discessit in partes ;
quas innumerabiles esse et parvas non oportet. Idem
euim vitii habet nimia, quod nulla divisio. Simile
confuso est, quicquid usque in pulverem sectum est.'"^
Under the second head, that is, as springing from ii. From
the relations of the Dividing Members to the Divided tionsVf the
Wholes, there are included the fourth and fifth laws. Member^s to
a Einst, 90. /3 Krug, Lorjik, § 126, Anm. 4.— Ed.
VOL. II. C
34) LECTURES ON LOGIC.
LECT. " As the notion and the notions into which it is di-
L_ vided, stand to each other in the relation of whole and
the Divided
Wholes.
parts, and as the whole is greater than the part, the
Fourth. fourth rule is manifestly necessary, viz. That no divid-
ing member of the predicate must by itself exhaust
the subject. When this occurs, the division is vicious,
or, more properly, there is no division. Thus the
division of raan into rational animals and unculti-
vated nations, would be a violation of this law.
Fifth. " On the other hand, as the notions into which a
notion is divided, stand to each other in the relation of
constituting parts to a constituted whole, and as the
whole is only the sum of all the parts, the necessity
of the fifth rule is manifest, — That the dividing mem-
bers of the predicate, taken together, must exhaust the
subject. For if this does not take place, then the
division of the principal notion has been only partial
and imperfect. We transgress this law, in the first
place, when we leave out one or more members of divi-
sion ; as for example, — The actions of men are either
good or had, — for to these we should have added or
indifferent. And in the second place, we transgress it
when we co-ordinate a subdivision with a division ; as
for example, — Philosophy is either theoretical ijhilo-
sophy or moral p)hilosophy : here the proper opposition
would have been theoretical philosophy and practical
philosophy.""' On the other hand, the dividing mem-
bers, taken together, must not do more than exhaust
the subject. The definition of the whole must apply
to every one of its parts, but this condition is not ful-
filled if there be a dividing member too much, that is,
if there be a notion brought as a dividing member,
which, however, does not stand in subordination to
a Esser, Logik, § 137.— Ed.
LECTURES ON LOGIC. 35
the divided whole. For example, — Mathematical fig- lect.
ures are either solids or surfaces [or lines or points']. '—
Here the two last members (lines and points) are re-
dundant and erroneous, for lines and points, though
the elements of mathematical figures, are not them-
selves figures.
Under the third head, as sprino;ino; from the rela- ni. From
, the rela-
tions of the several Dividing Members to Each Other, tions of the
there is a sino^le law, the sixth, which enjoins, — That Dividing
,,..,, . „ , . Members to
the dividmg members be reciprocally exclusive. Each other.
" As a division does not present the same but the dif-
ferent determinations of a single notion, (for otherwise
one and the same determination would be presented
twice), the dividing members must be so constituted
that they are not mutually coincident, so that they
either in whole or in part contain each other. This
law is violated when, in the first place, a subdivision
is placed above a division, as, — Philosophy is either
theoretical philosophy, or moral philosop)hy, or prac-
tical philosophy; here moral philosophy falls into
jyractical 2'>hilosophy as a subordinate part ; or when,
in the second place, the same thing is divided in dif-
ferent points of view, as, — Human actions are either
necessary, or free, or useful, or detrimental.'"^
Under the fourth and last head, as arising from the iv. From
relations of the Divisions to the Subdivisions, there is tions of the
contained one law, the seventh, which prescribes, — the Sub-
That the divisions proceed continuously from imme- seventh.
diate to mediate difierences, {Divisio ne fiat per saltum
vel hiatnm).
" As divisions originate in the character of a notion,
capable of an opposite determination, receiving this
determination, and as the subdivisions originate in
a Esser, Logik, § 137.— Ed.
XXV.
36 LECTUEES ON LOGIC.
LECT. these opposite determinations being themselves again
capable of opposite determinations, in which gradual
descent we may proceed indefinitely onwards, — from
this it is evident, that the divisions should, as far as
possible, be continuous, that is, the notion must first
be divided into its proximate, and then into its re-
moter parts, and this without overleaping any one
part ; or in other words, each part must be immedi-
ately subordinated to its whole."" Thus, when some
of the ancients divided philosophy into rational, and
natural, and moved, the first and second members are
merely subdivisions of theoretical philosophy, to which
moral as j^i'ci'Ctical p>hilosophy is opposed. Sometimes,
however, such a spring, — such a salt us, — is, for the sake
of brevity, allowed ; but this only under the express
condition, that the omitted members are interpolated
in thought. Thus, many mathematicians say, angles
are either right, or acute, or obtuse, although, if the
division were continuous, — without hiatus, it would
run, angles are either right or oblique; and the ob-
lique, again, either acute or obtuse.
a Esser, Lor/ik, § 1.37. — Ed.
LECTURES ON LOGIC. 37
LECTUEE XXVI.
METHODOLOGY.
SECTION TI. LOGICAL METHODOLOGY.
III. — DOCTRINE OF PROBATION.
We now proceed to the Third Part of Pure Meth- lect.
XXVI
odology, that which guides us to the third character
or virtue of Perfect Thinking,— the Concatenation of ^'■°^""°"-
Thought ; — I mean Probation, or the Leading of Proof.
I commence with the following paragraph : —
H LXXXVI. AVhen there are propositions or Par. lxxxvi.
judgments which are not intuitively manifest, -itsNatiie
and the truth of which is not admitted, thenments.
their validity can only be established when we
evolve it, as an inference, from one or more judg-
ments or propositions. This is called Probation,
Proving, or the Leading of Proof (prohatio, ar-
gumentatio, or demonstratio in its wider sense).
A Probation is thus a series of thoughts, in which
a plurality of different judgments stand to each
other, in respect of their validity, in the depend-
ence of determining and determined, or of ante-
cedents and consequents. In every Probation
there are three things to be distinguished, —
1°, The Judgment to be Proved, (thesis); 2°, The
XXVI.
88 LECTURES ON LOGIC.
LECT. Ground or Principle of Proof, (argumentum) ;
and, 3°, The Cogency of this principle to neces-
sitate the connection of antecedents and conse-
quents, {vis demonstrationis or nervus probandi).
From the nature of Probation, it is evident that
Probation without inference is impossible; and
that the Thesis to be proved and the Principles
of Proof stand to each other as conclusion and
premises, with this difference, that, in Probation,
there is a judgment (thesis) expressly supposed,
which in the Syllogism is not, at least necessarily,
the case."
Expiica- In regard to the terms here employed, it is to be
Terms em- noticcd that the term argumentation {argumentatio)
Ar|umenta- Is applied uot ouly to a reasoning of many syllogisms,
Argument, but likcwisc to a reasoning of one. The term argu-
ment {argumentum), in like manner, is employed not
only for the ground of a consecutive reasoning, but
for the middle term of a single syllogism. But it is,
moreover, vulgarly employed for the whole process of
argumentation.^
Demonstra- The term demonstration {demonstratio) is used in a
looser, and in a stricter, signification. In the former
sense, it is equivalent to 'prohation, or argumenta-
tion in general; in the latter, to necessary probation,
or argumentation from intuitive principles.
Leading of Thc cxpressiou leading of proof might, perhaps, be
sorts. translated by the term deduction, but then this term
must be of such a latitude as to include induction, to
which it is commonly opposed; for Probation may be
a Esser, Locjik, § 138. Cf. Krug, fang der Logik, § 32 et seq.']
Logik, § 127.— Ed. [Cf. Eichter, )3 See above, vol. i. p. 278.— Ed.
JJher den Gegenstand und den Urn-
LECTURES ON LOGIC. 39
either a process of Deduction, that is, the leading of lect.
proof out of one higher or more general proposition,
or a process of Induction, that is, the leading of proof
out of a plurality of lower or less general judgments.
To prove, is to evince the truth of a proposition not Probation
admitted to be true, from other propositions the truth
of which is already established. In every probation
there are three things to be distinguished : — l°,The Pro-
position to be Proved, — the Thesis; 2°, The Grounds
or Principle of Proof, — the Argument; and, 3°, The
Degree of Cogency with which the thesis is inferred
by the argumentum or argumenta, — the vis or nervus
'prohandi. All probation is thus syllogistic; but all How disUu-
syllogism is not probative. The peculiarity of proba- from Syiio-
tion consists in this, — that it expressly supposes a^'"™'
certain given proposition, a certain thesis, to be true ;
to the establishment of this proposition the proof is
relative; this proposition constitutes the conclusion
of the syllogism or series of syllogisms of which the
probation is made up : whereas, in the mere syllogistic
process, this supposition is not necessarily involved.
It is also evident that the logical value of a probation whereon
, , o r\ -x ^ c • • ' ^ depends tlie
depends, — 1 , (Jn the truth oi its principles or argu- logical value
menta, 2°, On their connection with each other and tion.
with the thesis or proposition to be proved, and, 3°,
On the logical formality of the inference of the thesis
from its argumenta. No proposition can be for an-
other the principle of proof, which is not itself either
immediately or mediately certain. A proposition is
immediately certain, or evident at first hand, when,
by the very nature of thought, we cannot but think
it to be true, and when it, therefore, neither requires
nor admits of proof. A proposition is mediately cer-
tain, or evident at second hand, when it is not at
40 LECTURES ON LOGIC.
LECT. once and in itself thoiiglit as necessarily true, but
•^^^^' when we are able to deduce it, with a consciousness
of certainty, from a proposition which is evident
at first hand. The former of these certainties is
called self-evident, iyituitive, original, ijrimm^ij, ulti-
mate, &c., and the latter, demonstrative, derivative,
secondary, &c.
Ground of Accordiug to this distinction, the Ground or Prin-
Ab^oiuteor ciplc of Proof is either absolute or relative. Ab-
solute, when it is an intuitive; relative, when it is
a demonstrative, proposition. That every proposition
must ultimately rest on some intuitive truth, — on some
judgment at first hand, is manifest, if the fact of pro-
bation itself be admitted; for otherwise the regress
would extend to infinity, and all probation, conse-
quently, be impossible. When, for example, in the
series of grounds H, G, F, E, D, C, B, there is no ulti-
mate or primary A, and when, consequently, every
A is only relatively, in respect of the consequent
series, but not absolutely and in itself, first; — in this
case, no sufficient and satisfactory probation is pos-
sible, for there always remains the question concern-
ing a still higher principle. But positively to show
that such primary judgments are actually given, is an
exposition which, as purely metaphysical, lies beyond
the sphere of Logic."
Distinction To tho gcucral form of a system of Proof belong the
tions*irre- followlug distinctious of propositions, to which I
general form formerly alluded,^ and which I may again recall to
of Proof!"" your remembrance. Propositions are either Tlieore-
and Practi- tical ov Practical. Practical, when they enounce the
way in which it is possible to effectuate or produce
a Compare Esser, Logik, § 138. — j3 See above, vol. i. p. 265. — Ed.
Ed.
LECTURES ON LOGIC. 41
something; Theoretical, when they simply enunciate lect.
a truth, without respect to the way in which this may '-
be realised or produced.''
A Theoretical proposition, if a primary or intuitive Axiom.
principle, is styled an Axiom. Examples of this are
given in the four Fundamental Laws of Logic, and in
the mathematical commonnotions — Theivlioleisgreater
than its part, — If equals he added to equals, the ivholes
are equal, &c. A Practical proposition, if a primary or Postulate.
intuitive principle, is styled a Postulate. Thus Geo-
metry postulates the possibility of drawing lines, — of
producing them ad iiifinitum, of describing circles, &c.
A Theoretical proposition, if mediate and demon- Theorem.
strable, is called a Theorem. This is laid down as a
Thesis, — as a judgment to be proved, — and is proved
from intuitive principles, theoretical and practical.
A Practical proposition, if mediate and demonstrable, Problem,
is called a Problem. In the probation, the Problem
itself is first enounced ; it is then shown in the solu-
tion how that which is required is to be done, — is
to be effected; and, finally, in the proof, it is demon-
strated that through this procedure the solution of
the problem is obtained. For example, in the geo-
metrical problem, — to describe an equilateral triangle
on a given straight line; — there this problem is first
stated; the solution then shows that, with thisplex, — if synthetic, the conclusion of the preceding syl-
logism is the subsumption of that following ; if analy-
tic, the conclusion of the preceding syllogism is the
sumption of that following. In respect of certainty,
both procedures are equal, and each has its peculiar
advantages ; in consequence of which the combination
of these two modes of proof is highly expedient. But
the Analytic Procedure is often competent where
the Synthetic is not ; Avhereas the Synthetic is never
possible where the Analytic is not, and this is
never possible where we have not a requisite stock of
propositions already verified. When the Probation is
partly analytic, partly synthetic, it is called Mixed.""'
P-;L^xxxviii. ^ LXXXVIII. The Formal Legitimacy of a
Legitimacy Probatlou Is determined by the foUowinp; rules.
01 a Proba- -^ ^
tion,— its 1 ° Nothin o; is to be beofo-ed, borrowed, or stolen ;
that is, nothing is to be presupposed as proved,
which itself requires a demonstration. The vio-
lation of this rule affords the vice called the
Petitio jyi'incijyii, or Fallacia qucesiti niedii {to Iv
a-f>yr\ alTelcrOai).^
2°, No proposition is to be employed as a prin-
ciple of proof, the truth of which is only to be
o Esser, Logil; § 142. — Ed. tV ttj apxji, id est, in principio; sed
jS [On error of this term, see tov iv apxy TrpoKfi/ufvov, id est, ejus
Pacius, Commentarius in Org. {In problematis, quod initio fuit proposi-
Anal. Prior ii. 16. " Non est pe- turn et in disquisitionem vocatum."
titio rfjs apxhs, id est, principii, vel Ibid, ii. 24. — Ed.]
LECTURES ON LOGIC. 51
evinced as a consequence of tlie proposition lect.
which it is employed to prove. The violation of — L.
this rule is the vice called varepov irpoTepov.
3°, No circular probation is to be made ; that
is, the proposition which we propose to prove
must not be used as a principle for its own pro-
bation. The violation of this rule is called the
Orhis vel circulus in demonstrando, — dicdlelus, —
6 oC aWrjkoiv rpoTTO?."
4°, No leap, no hiatus, must be made ; that is,
the syllogisms of which the probation is made up,
must stand in immediate or continuous connec-
tion. From the transgression of this rule results
the vice called the Saltiis vel Hiatus in demon-
strando.
5°, The scope of the probation is not to be
changed ; that is, nothing is to be proved other
than what it was proposed to prove. The violation
of this rule gives the Hetey^ozelesis, Ignoratio vel
Mutatio elenchi, and the Transitus in aluid
genus vel a genere ad genus, — /xera^Sao-is ets aWo
In this paragraph, I have mven, as different rules, These mies
, . , reduced to
those canons which are opposed to vices not abso-two.
lutely identical, and which have obtained different
denominations. But you must observe, that the first
three rules are all manifestly only various modifications
— only special cases, — of one general law. To this law,
likewise, the fourth rule may with perfect propriety
be reduced, for the saltvs or Jiiatus in prohando is, in
a See Sextus Empiricus, Pyrrh. ;8 [See Reinhold, Die Lorjilc odcr die
Hyp.,!. 169, ii. 68. Laertius, L. ix. allgemcine JJenl-forinenlehre, % 150, p.
§§ 88, 89. [Cf. Facciolati, Acroasis, 407, Jena, 1827.] [Cf. Krug, Lorjih,
V. p. 69 ct scq.] § 133. Esser, Locjih, § 144.— Ed.]
52
LECTURES ON LOGIC.
LECT.
XXVI.
Par.LXXXIX.
Rules of
Probation
reduced to
two.
fact, no less the assumption of a proposition as a prin-
ciple of probation which itself requires proof, than
either the petitio principi% the hysteron protei^on, or
the circulus in j)rohando. These five laws, therefore,
and the correspondent vices, may all be reduced to
two ; the one of which regards the means, — the
principles of proof; the other the end, — the propo-
sition to be proved. The former of these laws pre-
scribes, — That no proposition be employed as a prin-
ciple of probation, which stands itself in want of
proof ; the latter, — That nothing else be proved than
the proposition for whose proof the probation was in-
stituted. You may, therefore, add to the last para-
graph the following supplement : —
IT LXXXIX. These rules of the logicians may,
however, all be reduced to two.
1°, That no proposition be employed as a Prin-
ciple of Probation, which stands itself in need of
proof
2°, That nothing else be proved than the Pro-
position for whose proof the Probation was in-
stituted.
Explica-
tion.
First Rule.
Of these two, the former comprehends the first four
rules of the logicians, — the latter the fifth. I shall
now, therefore, proceed to illustrate the five rules in
detail.
The First Rule — Nothing is to be begged, borrowed,
or stolen ; that is, nothing is to be presupposed as
proved, which itself requires a demonstration,- — is, in
fact, an enunciation of the first general rule I gave
you, and to this, therefore, as we shall see, the second,
third, and fourth are to be reduced as special appli-
LECTURES ON LOGIC. 53
cations. But, in considering this law In its univer- lect.
. . XXVI
sality, it is not to be understood as if every probation — 1 — L
were at once to be rejected as worthless, in which un£^i!lch
anything is presupposed and not proved. Were this Jo'be^,^der-
its sense, it would be necessary in every probation to ^**""^'
ascend to the highest principles of human knowledge,
and these themselves, as immediate and, consequently,
incapable of proof, might be rejected as unproved
assumptions. Were this the meaning of the law,
there could be no probation whatever. But it is not
to be understood in this extreme rigour. That pro-
bation alone is a violation of this law, and, conse-
quently, alone is vicious, in which a proposition is
assumed as a principle of proof, which may be doubted
on the ground on which the thesis itself is doubted,
and where, therefore, we prove the uncertain by the
equally uncertain. The probation must, therefore,
depart from such principles as are either immediately
given as ultimate, or mediately admit of a proof from
other sources than the proposition itself in question.
When, for example, it was argued that the Newtonian
theory is false, which holds colours to be the result
of a diversity of parts in light, on the ground, ad-
mitted by the ancients, that the celestial bodies, and,
consequently, their emanations, consist of homoge-
neous elements ; — this reasoning was inept, for the
principle of proof was not admitted by modern
philosophers. Thus, when Aristotle defends the in-
stitution of slavery as a natural law, on the ground
that the barbarians, as of inferior intellects, are the
born bondsmen of the Greeks, and the Greeks, as of
superior intellect, the born masters of the barbarians,"
o Polit., i. 2.— Ed.
54 LECTURES ON LOGIC.
•LECT. — (an argument which has, likeAvise, been employed
in modern times in the British Parliament, with the
substitution of negroes for barbarians, and whites
for Greeks), — this argument is invalid, as assuming
what is not admitted by the opponents of slavery.
It would be a petitio principii to prove to the Mo-
hammedan the divinity of Christ from texts in the
New Testament, for he does not admit the authority
of the Bible ; but it would be a valid argumentum
ad hominem to prove to him from the Koran the pro-
phetic mission of Jesus, for the authority of the Koran
he acknowledges.
Second The Second Eule, That no proposition is to be em-
ployed as a principle of proof, the truth of which is
only to be evinced as a consequence of the proposi-
tion which it is employed to prove, — is only a special
case of the preceding. For example, if we were to
argue that man is a free agent, on the ground that
he is morally responsible for his actions, or that his
actions can be imputed to him, or on the ground
that vice and virtue are absolutely different, — in these
cases, the hysteron p)roteron is committed ; for only
on the ground that the human will is free, can man
be viewed as a morally responsible agent, and his ac-
tions be imputed to him, or can the discrimination of
vice and virtue, as more than a merely accidental rela-
tion, be maintained. But we must pause before we
reject a reasoning on the ground of hysteron proteron;
for the reasoning may still be valid, though this logi-
cal fault be committed. Nay, it is frequently neces-
sary for us to reason by such a regress. In the very
example given, if we be unable to prove directly that
the will of man is free, but are able to prove that he
is a moral agent, responsible for his actions, as sub-
LECTURES ON LOGIC. 55
jectecl to tlie voluutaiy but unconditioned Law of lect.
Duty, and if the fact of this law of duty and its uu- — "- — L
qualified obligation involve, as a postulate, an eman-
cipation from necessity, — in that case, no competent
objection can be taken to this process of reasoning.
This, in fact, is Kant's argument. From what he calls
the categorical imi^erative, that is, from the fact of
the unconditioned law of duty as obligatory on man,
he postulates, as conditions, the liberty of the human
will, and the existence of a God, as the moral gover-
nor of a moral universe.*
The Third Law,^ — That no circular probation is to Third Rule,
be made, that is, the proposition which we propose to
23rove must not be used as a principle for its own pro-
bation, — this, in like manner, is only a particular case
of the first. " To the Circle there are required properly
two probations, which are so reciprocally related that
the antecedent in the one is proved by its own conse-
quent in the other. The proposition A is true be-
cause the proposition B is true ; and the proposition
B is true because the proposition A is true. A circle
so palpable as this would indeed be committed by no
one. The vice is usually concealed by the interpola-
tion of intermediate propositions, or by a change in
the expression."'^ Thus Plato, in his Phcedo^ demon-
strates the immortality of the soid from its simplicity ;
and, in the Republic,^ he demonstrates its simplicity
from its immortality.
In relation to the Ilysteron Proteron and the Circle, Regressive
I must observe that these present some peculiar diffi- gressive
. o ^ Proofs not
culties for the systematic arrangement oi our know- to be con-
a Kritih der veinen Yernunft, Me- j3 Krug, Loijil; § 133. Anm. 3. —
thodenlehre, Hauptst., ii. Abschn., 2. Ed.
Kritik der praktischen Vernunft, p. y P. 78. — Ed.
274, ed. Rosenkranz.— Ed. S B. x. p. 611.— Ed.
56 LECTURES ON LOGIC.
LEOT. ledo-e. Throu2;li the Circle, (the result of which is only
the proof of an assertion), — through the circle by itself,
finin.ici nothino- whatever is gained for the logical develop-
with tlio O c^ <zj ■*•
Scic"^''''^ ment of our knowledge. But we must take care not
to confound the connection of Regressive and Pro-
gressive Proofs with the tautological Circle. AVhen,
in the treatment of a science out of the observed
facts, we wish to generalise universal laws, we lead,
in the first place, an inductive probation, that (ort)
certain laws there are. Having assured ourselves of
the existence of these laws by this regressive process,
we then place them in theory at the head of a pro-
gressive or synthetic probation, in which the facts
again recur, reversed and illustrated from the laws,
which, in the antecedent process, they had been em-
ployed to establish ; that is, it is now shown why
(Stort) these facts exist.
Fourth The Fourth Rule, — No leap, no gap, must be made,
that is, the syllogisms of which the probation is made
up must stand in immediate or continuous connection,
• — may be, likewise, reduced to the first. For here
the only vice is that, by an ellipsis of an intermediate
link in the syllogistic chain, we use a proposition which
is actually without its proof, and it is only because
this proposition is as yet unproved, that its employ-
ment is illegitimate. The Saltus is, therefore, only a
special case of the Petitio.
The Saltus The Soltus is committed when the middle term of
'siraudu.'' one of the syllogisms in a probation is not stated.
If the middle term be too manifest to require state-
ment, then is the saltus not to be blamed, for it is
committed only in the expression and not in the
thought. If the middle term be not easy of dis-
covery, then the saltus is a fault ; but if there be
LECTURES ON LOGIC. 57
no middle term to be found, then the scdtus is a vice lect,
which invalidates the whole remainder of the proba- L
tion. The proper saltus, — the real violation of this
law, is, therefore, when we make a transition from one
proposition to another, the two not being connected
together as reason and consequent." The (vulgar)
Enthymeme and the Sorites do not, therefore, it is
evident, involve violations of this law.
The Fifth Eule, — The scope of the probation is not Fifth Rule,
to be changed, that is, nothing is to be proved other
than what was proposed to be proved, — corresponds
to the second of the two rules which I gave, and of
which it is only a less explicit statement. It evidently Admits of
admits of three kinds or degrees. In the first case, grees.
the proposition to be proved is changed by the
change of its subject or predicate into different no-
tions. Again, the proposition may substantially re-
main the same, but may be changed into one either of
a wider or of a narrower extension, — the second and
third cases.
The first of these cases is the Mutatio Elenchi, or First
Transitus ad aliud genus, properly so called. " When Mltatlo
a probation does not demonstrate what it ought to^^^"^*"'"*
demonstrate, it may, if considered absolutely or in
itself, be valid ; but if considered relatively to the pro-
position which it behoves us to prove, it is of no value.
We commute by this procedure the whole scope or pur-
port of the probation ; we desert the proper object of
inquiry, — the point in question. If a person would
prove the existence of ghosts, and to this end prove
by witness the fact of unusual noises and appear-
ances during the night, he would prove something
very dijfferent from what he proposed to establish ;
a Of. Krug, Logik, § 133. Anm. 4.— Ed.
58 LECTURES ON LOGIC.
LECT. for this Avoiild be admitted without difficulty hj those
XXVI
who still denied the apparition of ghosts : it, therefore,
behoved him to show that the unusual phoenomena
were those of a spirit good or bad." "
Second Dc- The two other cases, — when the proposition actually
whk'rto''o proved is either of a smaller or of a greater extension
proved than the proposition which ought to have been proved,
— are not necessarily, like the preceding, altogether
irrelevant. They are, however, compared together, of
various degrees of relevancy. In the former case,
where too little is proved, — here the end proposed is,
to a certain extent at least, changed, and the proba-
tion results in somethino; different from what it was
intended to accomplish. For example, if we propose
to prove that Sempronius is a virtuous character,
and only prove the legality of his actions, we here
prove something less than, something different from,
what we professed to do ; for we proposed to prove
the internal morality, and not merely the external law-
fulness, of his conduct. Such a proof is not absolutely
invalid ; it is not even relatively null, for the exter-
nal legality is ahvays a concomitant of internal mor-
ality. But the existence of the latter is not evinced
by that of the former, for Sempronius may conform
his actions to the law from expediency and not from
duty.^
Third De- 111 the other case, in which there is proved too much,
ihfciTtoo the probation is lawful, and only not adequate and
proved.' precise. For example, if we propose to prove that the
soul does not perish with the body, and actually prove
that its dissolution is absolutely impossible, — here
the proof is only superabundant. The logical rule, —
o Krug, Loc/ik, % 133. Anm. 2.— ;3 Cf. Krug, Lor/ik, § 133. Anm. 5.
Ed. —Ed.
LECTURES ON LOGIC. 59
Qui nimium 2')'i'ohat, nihil probat, is, therefore, in its lect.
universal or unqualified expression, incorrect. The — ^ — '-
proving too much is, however, often the sign of a
saltus having been committed. For example, — when
a religious enthusiast argues from the strength of his
persuasion, that he is, therefore, actuated by the Holy
Spirit, and his views of religion consequently true, —
there is here too much proved, for there is implied
the antecedent, omitted by a saltus, that whoever is
strongly persuaded of his inspiration is really inspired,
— a proposition too manifestly absurd to bear an ex-
plicit enouncement. In this case, the apparent too
much is in reality a too much which, when closely
examined, resolves itself into a nothing."
We have thus terminated the consideration of Pure
or Abstract Logic, in both its Parts, and now enter on
the Doctrine of Modified or Concrete Logic.
a [Cf. Sigwart, Ilandbuch zu Vorksungen iiher die Logik, § 407, p. 252.]
60 LECTURES ON LOGIC.
LECTURE XXVII.
MODIFIED LOGIC.
PART I. — MODIFIED STOICHEIOLOGY.
SECTION I. — DOCTRINE OF TRUTH AND ERROR.
TRUTH. ITS CHARACTER AND KINDS.
LECT. Having now terminated tlie Doctrine of Pure or Ab-
'- stract Logic, we proceed to that of Modified or Con-
Logtc!— Crete Logic. In entering on this subject, I have to
Its object. j,QQ^ii ^Q jQ^^Y memory what has formerly been stated
in regard to the object which Modified Logic pro-
poses for consideration. Pure Logic takes into ac-
count only tlie necessary conditions of thought, as
founded on the nature of the thinking process itself.
Modified Logic, on the contrary, considers the condi-
tions to which thought is subject, arising from the
empirical circumstances, external and internal, under
which exclusively it is the will of our Creator that
man should manifest his faculty of thinking. Pure
Logic is thus exclusively conversant with the form ;
Modified Logic is, likewise, occupied with the matter,
of thought. And as their objects are difterent, so,
likewise, must be their ends. The end of Pure Logic
is formal truth, — the harmony of thought with
thought ; the end of Modified Logic is the harmony
of thought with existence. Of these ends, that which
Pure Logic proposes is less ambitious, but it is fully
and certainly accomplished ; the end which Modified
LECTURES ON LOGIC. Gl
Logic proposes is higher, but it is far less perfectly lect!
attained. The problems which Modified Logic has to ' ^
solve may be reduced to three: 1°, What is Truth Lmslie-
and its contradictory opposite, — Error ? 2°, What fhree'I *"
are the Causes of Error and the Lnpediments to Truth,
by which man is beset in the employment of his facul-
ties, and what are the Means of their Removal ? And,
3°, What are the Subsidiaries by which Human
Thought may be strengthened and guided in the
exercise of its functions 1
From this statement it is evident that Concrete And distri-
Loo;ic miolit, like Pure Lome, have been divided into tween its
a Stoicheioloey and a Metliodolosy, — the former com- lo^v and its
prismg the tirst two heads, — the latter the third, r or oiogy.
if to Modified Stoicheiology we refer the considera-
tion of the nature of concrete truth and error, and of
the conditions of a merely not erroneous employment
of thought, — this will be exhausted in the First and
Second Chapters ; whereas if we refer to Methodology
a consideration of the means of employing thought
not merely without error but with a certain positive
perfection, — this is what the Third Chapter professes
to expound.
I commence the First Chapter, which proposes to
answer the question, — What is Truth 'i with its cor-
relatives, — by the dictation of the following paragraj)h.
H XC. The end which all our scientific efi'orts Par. xc.
are exerted to accomplish, is Truth and Cer- Certainty,
m 1 • 1 1 — what.
tamty. Irutn is the correspondence or agree-
ment of a cognition with its object ; its Criterion
is the necessity determined by the laws which
govern our faculties of knowledge ; and Certainty
is the consciousness of this necessity." Certainty,
o Cf. Twesten, I>ie Lofjik, inhe.ondcre die Analyiik, § 306. — Ed.
62 LECTURES ON LOGIC.
LECT, or the conscious necessity of knowledge, abso-
'- lutely excludes the admission of any opj)osite
supposition. Where such appears admissible,
doubt and uncertainty arise. If we consider
truth by relation to the degree and kind of Cer-
tainty, we have to distinguish Knowledge, Belief,
and Oimiion. Knowledge and Belief differ not
only in degree but in kind. Knowledge is a
certainty founded upon insight ; Belief is a cer-
tainty founded upon feeling. The one is per-
spicuous and objective ; the other is obscure and
subjective. Each, however, supposes the other ;
and an assurance is said to be a knowledge or
a belief, according as the one element or the other
preponderates. Opinion is the admission of
something as true, where, however, neither in-
sight nor feeling is so intense as to necessitate a
perfect certainty. What prevents the admission
of a proposition as certain is called Doubt. The
approximation of the imperfect certainty of
opinion to the perfect certainty of knowledge or
belief is called Prohahility,
If we consider Truth with reference to Know-
ledge, and to the way in which this knowledge
arises, we must distinguish Empirical or a 'pos-
teriori, from Pure or a ^^riori Truth. The former
has reference to cognitions which have their
source in the presentations of Perception, Ex-
ternal and Internal, and which obtain their form
by the elaboration of the Understanding or Fa-
culty of Relations [hidvoia.) The latter is con-
tained in the necessary and universal cognitions
afforded by the Regulative Faculty, — Intellect
Proper, — or Common Sense, (voOs.)
LECTURES ON LOGIC. G3
This paragrapli, after stating that Truth and Cer- lect.
tainty constitute the end of all our endeavours after
knowledge, for only in the attainment of truth and ^^l]"^^'
certainty can we possibly attain to knowledge or
science ; — I say, after the statement of this manifest
proposition, — it proceeds to define what is meant by
the two terms Ti'utli and Certainty ; and, to com-
mence with the former, — Truth is defined, the corre-
spondence or agreement of a cognition or cognitive act
of thought with its object.
The question — What is Truth 1 is an old and cele- Truth,—
brated problem. It was proposed by the Roman
Governor, — by Pontius Pilate, — to our Saviour ; and it
is a question which still recurs, and is still keenly agi-
tated in the most recent schools of Philosophy. In one Definition
. ^ ^ _ . of the term,
respect, all are nearly agreed m regard to the deiini-
tion of the term, for all admit that by truth is under-
stood a harmony, — an agreement, — a correspondence
between our thought and that which we think about.
This definition of truth we owe to the schoolmen.
" Veritas intellectus," says Aquinas, "est adcequatio in-
tellectus et rei, secundum quod intellectus elicit esse,
quod est, vel non esse, quod non est." " From the
schoolmen, this definition had been handed down to
modern philosophers, by whom it is currently em-
ployed, without, in general, a suspicion of its origin.
It is not, therefore, in regard to the meaning of the
term truth, that there is any difi'erence of opinion
among philosophers. The questions which have pro- Questions
voked discussion, and which remain, as heretofore, regarding
without a definitive solution, are not whether truth be
a [Contra Gentiles, lib. i.e. 59. See Ruiz, Comment, de Scicntia, de Ideis,
Biunde, t/ber Wahrlieit in Erhennen, de Veritate, &c. Disp. Ixxxv., p. 871
p. 11. On Truth in general, see et seq.]
64! LECTUKES ON LOGIC.
LECT. tlie harmony of thought and reality, but whether this
L harmony, or truth, be attainable, and whether we pos-
sess any criterion by which we can be assured of its
attainment. Considering, however, at present only the
meaning of the term, philosophers have divided Truth,
(or the harmony of thought audits object), into differ-
ent species, to which they have given diverse names ;
but they are at one, neither in the division nor in the
nomenclature.
For man It is plain that for man there can only be conceived
kiwis of two kinds of Truth, because there are for human thousrht
Trutli,— . . . ^
Formal and Quly two spcclcs of objcct. For that about which we
think, must either be a thought, or something which a
thought contains. On this is founded the distinction
of Formal Knowledge and Real Knowledge, — of For-
mal Truth and Real Truth. Of these in their order.
I. Formal I. lu regard to the former, a thouo;ht abstracted
from what it contains, that is, from its matter or what
it is conversant about, is the mere form of thought.
The knowledge of the form of thought is a formal
knowledge, and the harmony of thought with the form
Formal of thought is, conscquently. Formal Truth. No w Formal
Truth of . .
two kinds, Knowled2:e is of two kinds : for it reo;ards either the
—Logical T . /. 1 .
andMathe- couditious of tlic Elaborativc Faculty, — the Faculty
matical. r>rni tt^ t- t-w
of Thought Proper, — or the conditions of our Presen-
tations or Representations of external things, that is,
the intuitions of Space and Time. The former of these
sciences is Pure Logic, — the science which considers
the laws to which the Understanding is astricted in its
elaborative operations, without inquiring what is the
object, — what is the matter, to which tliese operations
are applied. The latter of these sciences is Mathema-
tics, or the science of Quantity, which considers the re-
lations of Time and Space, without inquiring whether
LECTURES ON LOGIC. 65
there be any actual reality in space or time. Formal lect.
. . XXVII
truth will, therefore, be of two kinds, — Logical and — '-
Mathematical. Logical truth is the harmony or agree- Logical
ment of our thoughts with themselves as thoughts, in
other words, the correspondence of thought with the
universal laws of thinking. These laws are the object
of Pure or General Logic, and in these it places the cri-
terion of truth. This criterion is, however, only the nega-
tive condition — only the conditio sine qua non, of truth.
Logical truth is supposed in supposing the possibility
of thought ; for all thought presents a combination, the
elements of which are repugnant or congruent, but
which cannot be repugnant and congruent at the same
time. Logic might be true, although we possessed no
truth beyond its fundamental laws ; although we knew
nothing of any real existence beyond the formal hypo-
thesis of its possibility.
But were the I-iaws of Logic purely subjective, that
is, were they true only for our thought alone, and
without any objective validity, all human sciences,
(and Mathematics among the rest), Avould be purely
subjective likewise ; for we are cognisant of objects
only under the forms and rules of which Logic is the
scientific development. If the true character of ob-
jective validity be universality, the laws of Logic are
really of that character, for these laws constrain us,
by their own authority, to regard them as the univer-
sal laws not only of human thought, but of universal
reason.
The case is the same with the other formal science, Mathemati
the science of Quantity, or Mathematics. Without ^^'^
inquiring into the reality of existences, and without
borrowing from or attributing to them anything,
Arithmetic, the science of Discrete Quantity, creates
VOL. II. E
QQ LECTURES ON LOGIC.
LECT. its numbers, and Geometry, the science of Continuous
XWII
— '- Quantity, creates its figures ; and botli operate upon
these their objects in absolute independence of all
external actuality. The two mathematical sciences
are dependent for their several objects only on the
notion of time and the notion of space, — notions under
which alone matter can be conceived as possible, for
all matter supposes space, and all matter is moved in
space and in time. But to the notions of space and time
the existence or non-existence of matter is indifferent ;
indifferent, consequently, to Geometry and Arithmetic,
so long at least as they remain in the lofty regions of
pure speculation, and do not descend to the practical
application of their principles. If matter had no exist-
ence, nay, if space and time existed only in our minds,
mathematics would still be true ; but their truth would
be of a purely formal and ideal character, — would fur-
nish us with no knowledge of objective realities."
So much for Formal Truth, under its two species of
Logical and Mathematical
Trut?'^^ The other genus of truth, — (the end which the Real
Sciences propose), — is the harmony between a thought
Real and aud its matter. The Real Sciences are those which
Sciences, liavG a determinate reality for their object, and which
are conversant about existences other than the forms
of thought. The Formal Sciences have a superior
certainty to the real ; for they are simply ideal com-
binations, and they construct their objects without
inquiring about their objective reality. The real sci-
ences are sciences of fact, for the point from which
they depart is always a fact, — always a presentation.
Some of these rest on the presentations of Self-con-
o Cf. E8ser, Lof/ik, § 172.— Ed. [Fries, Lo(/ik, § 124.]
LECTURES ON LOGIC. 67
sciousness, or the facts of miud : others on the pre- lect,
XXVII.
sentations of Sensitive Perception, or the facts of -
nature. The former are the Mental Sciences, the Real Sci-
hatter the Material. The facts of mind are given iuciuded'^the
partly as contingent, partly as necessary ; the latter, — Matei^iai."
the necessary facts, — are universal virtually and in
themselves ; the former, — the contingent facts, — only
obtain a fictitious universality by a process of gener-
alisation. The facts of nature, however necessary in
themselves, are given to us only as contingent and
isolated phsenomena; they have, therefore, only that
conditional, that empirical, generality, which we bestow
on them by classification.
Real truth is, therefore, the correspondence of our How can we
thoughts with the existences which constitute their there is a
, . -r~> 1 T rv ^ • TT correspouJ-
objects. But here a dimculty arises; — How can we eme be-
know that there is, that there can be, such a corre- thought and
spondence'? All that we know of the objects is through '^° ^^'^ '
the presentations of our faculties ; but whether these
present the objects as they are in themselves, we can
never ascertain, for to do this it would be requisite to
go out of ourselves, — out of our faculties, — to obtain a
knowledge of the objects by other faculties, and thus
to compare our old presentations with our new. But
all this, even were the supposition possible, would be
incompetent to afford us the certainty required. For
were it possible to leave our old, and to obtain a new,
set of faculties, by which to test the old, still the
veracity of these new faculties would be equally ob-
noxious to doubt as the veracity of the old. For
what guarantee could we obtain for the credibility in
the one case, which we do not already possess in the
other 1 The new faculties could only assert their own
truth ; but this is done by the old; and it is impos-
68 LECTURES ON LOGIC.
LECT. sible to imagine any presentations of the non-ego by
^ '- any finite intelligence, to which a doubt might not be
raised, whether these presentations were not merely
subjective modifications of the conscious ego itself.
All that could be said in answer to such a doubt is,
that if such were true, our whole nature is a lie, — a
supposition w^hich is not, without the strongest evi-
dence, to be admitted ; and the argument is as com-
petent against the sceptic in our present condition, as
it would be were we endowed with any other con-
ceivable form of Acquisitive and Cognitive Faculties.
But I am here trench hig on what ought to be re-
served for an explanation of the Criterion of Truth.
Real Such, as it appears to me, is the only rational divi-
it™ubcirvi- sion of Truth, according to the different character of
the objects to which thought is relative, — into Formal
and into Real Truth. Formal Truth, as we have seen,
is subdivided into Logical and into Mathematical.
Real Truth might likewise be subdivided, were this
Metapiiysi- rcquisitc, into various species. For example. Meta-
physical Truth might denote the harmony of thought
Psychoiogi- with the necessary facts of mind ; Psychological
Truth, the harmony of thought with the contingent
Physical, facts of miud ; and Physical Truth, the harmony of
thought with the phcenomena of external experience.
Various ap- It uow rcmaius to say a word in regard to the con-
the term fuslou which has bccu introduced into this subject, by
the groundless distinctions and contradictions of philo-
sophers. Some have absurdly given the name of iridh
to the mere reality of existence, altogether abstracted
from any conception or judgment relative to it, in any
intelligence human or divine. In this sense physical
truth has been used to denote the actual existence of
a thing. Some have given the name of mctcipliysical
I
LECTURES ON LOGIC. 69
truth to the con2:ruence of tlie thino; with its idea in lect.
XXVII
the mind of the Creator. Others again have bestowed '-
the name of metaphysical truth on the mere logical
possibility of being thought ; while they have deno-
minated by logical truth the metaphysical or physical
correspondence of thought with its objects. Finally,
the term moral or ethical truth has been given to
veracity, or the correspondence of thought with its
expression. In this last case, truth is not, as in the
others, employed in relation to thought and its object,
but to thouo;ht and its enouncement. So much for the
notion, and the principal distinctions of Truth.
But returnino; to the parao-raph, I take the next The crite-
'^ 1-1 rionof
clause, which is, — ' The Criterion of truth is the neces- Truth,
sity determined by the laws which govern our faculties
of knowledge ; and the consciousness of this necessity is
certainty.' That the necessity of a cognition, that
is, the impossibility of thinking it other than as it
is presented, — that this necessity, as founded on the
laws of thought, is the criterion of truth, is shown
by the circumstance, that where such necessity is
found, all doubt in regard to the correspondence of
the cognitive thought and its object must vanish ;
for to doubt whether what we necessarily think in a
certain manner, actually exists as we conceive it, is
nothing less than an endeavour to think the necessary
as the not necessary or the impossible, which is con-
tradictory.
What has just been said also illustrates the truth of
the next sentence of the paragraph, — viz. ' Certainty or
the conscious necessity of a cognition absolutely ex-
cludes the admission of any opposite supposition.
When such is found to be admissible, doubt and un-
certainty arise.' This sentence requiring no explan-
70 LECTURES ON LOGIC.
LECT. ation, I proceed to the next — viz., * If we consider
•^^^"' truth by relation to the degree and kind of Certainty,
we have to distinguish Knowledge, Belief, and Opinion.
Knowledge and Belief differ not only in degree but
in kind. Knowledge is a certainty founded on intui-
tion. Belief is a certainty founded upon feeling. The
one is perspicuous and objective, the other is obscure
and subjective. Each, however, supposes the other,
and an assurance is said to be a knowledge or a belief,
according as the one element or the other prepon-
derates.'
Knowledge In reference to this passage, it is necessary to say
— their dif- something in regard to the difference of Knowledge
and Belief. In common language the word Belief is,
often used to denote an inferior degree of certainty.
That the We may, however, be equally certain of what we be-
au know-° lieve as of what we know, and it has, not without
ultimately ground, bccu maintained by many philosophers, both
intoa'cer- vci aucicut aud in modern times, that the certainty of
Belief, all knowledge is, in its ultimate analysis, resolved into
by Luther, a ccrtaiuty of belief. " All things," says Luther, " stand
in a belief, in a faith, which we can neither see nor
comprehend. The man who would make these visible,
manifest and comprehensible, has vexation and heart-
grief for his reward. May the Lord increase Belief in
you and in others." ° But you may perhaps think that
the saying of Luther is to be taken theologically, and
that, philosophically considered, all belief ought to be
founded on knowledo;e, not all knowledo-e in belief.
But the same doctrine is held even by those philo-
sophers who are the least disposed to mysticism or
Aristotle, blind faith. Among these Aristotle stands distin-
a Wchhclt, Th. iii. Abth. 2. Worls, p. 778.— Ed.
Quoted by Sir W. Hamilton, RdiVs
LECTUKES ON LOGIC. 71
giiisbecL He defines science, strictly so called, or the lect.
knowledge of indubitable truths, merely by the inten- — 1
sity of our conviction or subjective assurance ; "" and
on a primary and incomprehensible belief he hangs
the whole chain of our comprehensible or mediate
knowledge. The doctrine which has been called The
Philosophy of Common Sense, is the doctrine which
founds all our knowledge on belief ; and, though this
has not been signalised, the doctrine of Common Sense
is perhaps better stated by the Stagirite than by
any succeeding thinker. " "What," he says, " appears
to all men, that we affirm to be, and he who rejects
this belief (Trtcrrt?) will assuredly advance nothing
better worthy of credit." This passage is from his
Nicomachean Etldcs.^ But, in his Physical Treatises,
he founds in belief the knowledge we have of the re-
ality of motion, and by this, as a source of knowledge
paramount to the Understanding, he supersedes the
contradictions which are involved in our conception
of motion, and which had so acutely been evolved by
the Eleatic Zeno, in order to show that motion was
impossible."^ In like manner, in his Logical Treatises,
Aristotle shows that the primary or ultimate princi-
ples of knowledge must be incomprehensible ; for if
comprehensible, they must be comprehended in some
higher notion, and this again, if not itself incompre-
hensible, must be again comprehended in a still higher,
and so on in a progress ad iiifinitimi, which is absurd.^
But what is given as an ultimate and incomprehen-
sible principle of knowledge, is given as a fact, the exist-
a Various passages from Aristotle 7 B. viii. c. 3. See RekVs Worlcs,
to this effect are cited by the Author, ^. 773. — Ed.
Re'id's Worlcs, p. 771. — Ed. 5 Mctaphys., iii. (iv.) i. Cf. Anal.
& B. X. c, 2.— Ed. Post, i. 2, 3.— Ed.
72 LECTURES ON LOGIC.
LECT. ence of whicli we must admit, but the reasons of whose
■^ '- existence we cannot know, — we cannot understand.
But such an admission, as it is not a knowledge, must
be a belief ; and thus it is that, according to Aristotle,
all our knowledge is in its root a blind, a passive faith,
in other words, a feeling. The same doctrine was
subsequently held by many of the acutest thinkers of
The riaton- aucicnt times, more especially among the Platonists ;
Procius. and of these Proclus is perhaps the philosopher in
whose works the doctrine is turned to the best account."
In modern times we may trace it in silent operation,
though not explicitly proclaimed, or placed as the
foundation of a system. It is found spontaneously
recognised even by those who might be supposed the
least likely to acknowledge it without compulsion.
Hume. Hume, for example, against whose philosophy the
doctrine of Common Sense was systematically ar-
rayed, himself pointed out the weapons by which his
adversaries subsequently assailed his scepticism ; for
he himself was possessed of too much philosophical
acuteness not to perceive that the root of knowledge
is belief. Thus, in his Inquiry, he says — " It seems
evident that men are carried by a natural instinct
or prepossession to repose faith in their senses : and
that, without any reasoning, or even almost before the
use of reason, we always suppose an external universe
which depends not on our preception, but would exist
though we and every sensible creature were absent or
annihilated. Even the animal creation are governed
by a like opinion, and preserve this belief, — the belief
of external objects, in all their thoughts, designs, and
actions .... This very table, which we see
o III Platoiiis Theologiam, i. c. 25. Quoted in Rekl's Works, p. 776. — Eij.
LECTURES ON LOGIC. 73
wliite, and which we feel hard, is believed to exist lect.
XXVIT
independent of our perception, and to be something
external to our mind which perceives it." *
But, on the other hand, the manifestation of this The mani-
•11 11 r festation of
belief necessaruy involves knowledge ; lor we cannot Belief in-
believe without some consciousness or knowledge of Knowledge.
the belief, and, consequently, without some conscious-
ness or knowledge of the object of the belief. Now,
the immediate consciousness of an object is called an intuition, -
what.
intuition, — an insight. It is thus impossible to separ-
ate belief and knowledge, — feeling and intuition.
They each sui3pose the other.
The consideration, however, of the relation of Belief The qucs-
111 T • ^^^^ ^^ '**
and Knowledo;e does not properly belong; to Lome, the relation
'^ .. rr./ '^ '^of Belief
except in so far as it is necessary to explain the nature an<i Kuow-
. lodge pro-
of Truth and Error, It is alto2;ether a metaphysical periy mcta-
. , physical.
discussion ; and one of the most difficult problems of
which Metaphysics attempts the solution.
The remainder of the paragraph contains the state-
ment of certain distinctions and the definition of cer-
tain terms, which it was necessary to signalise, but
which do not require any commentary for their illus-
tration. The only part that might have required an
explanation is the distinction of Truth into Pure, or
a 2^'>'iori, and into Empirical, or a posteriori. The
explanation of this division has been already given
more than once in the course of the Lectures,^ but the
following may now be added.
Experience presents to us only individual objects, Pme and
1 , .-,..-,-,-,. .-. .1 Empirical
and as these individual objects might or might not Truth.
a Inquiry concerning the Human ^)A_f/s/cs, vol. ii. p. 194 et seq. Cf.
Understanding, sect. 12. Philosophi- Esser, Logik, §§ 4, 171. — Ed. [Fries,
cal Works, iv. p. 177.— Ed. Logik, % 124.]
/3 See above, Lectures on Meta-
74 LECTURES ON LOGIC.
LECT. have come within our sphere of observation, our whole
'^"^^"' knowledge of and from these objects might or might
not exist ; — it is merely accidental or contingent. But
as our knowledge of individual objects affords the
possibility, as supplying the whole contents, of our
generalised or abstracted notions, our generalised or
abstracted notions are, consequently, not more neces-
sary to thought, than the particular observations out of
which they are constructed. For example, every horse
I have seen I might not have seen ; and I feel no more
necessity to think the reality of a horse than the
reality of a hippogriff ; I can, therefore, easily anni-
hilate in thought the existence of the whole species.
I can suppose it not to be, — not to have been. The
case is the same with every other notion which is
mediately or immediately the datum of observation.
We can think away each and every part of the know-
ledge we have derived from experience ; our whole em-
pirical knowledge is, therefore, a merely accidental
possession of the mind.
But there are notions in the mind of a very different
character, — notions which we cannot but think, if we
think at all. These, therefore, are notions necessary
to the mind ; and, as necessary, they cannot be the
product of experience. For example, I perceive some-
thing to begin to l)e. I feel no necessity to think
that this thing must be at all, but thinking it exist-
ent, I cannot but think that it has a cause. The no-
tion, or rather the judgment, of Cause and Effect is,
therefore, necessary to the mind. If so, it cannot be
derived from experience.
LECTURES ON LOGIC. 75
LECTUEE XXVIII.
MODIFIED STOICHEIOLOGY.
SECTION I. — DOCTRINE OF TRUTH AND ERROR.
SECTION II. ERROR, ITS CAUSES AND REMEDIES.
A. — GENERAL CIRCUMSTANCES — SOCIETY.
I NOW proceed to the consideration of the opposite lect.
... XXVIII.
of Truth, — Error, and, on this subject, give you the
following paragraph.
H XCI. Error is opposed to Truth ; and Error Par. xci.
arises, 1°, From the commutation of what is Sub- charaJter
jective with what is Objective in thought ; —
2°, From the Contradiction of a -supposed know-
ledge with its Laws; or, 3°, From a want of Ade-
quate Activity in our Cognitive Faculties.
Error is to be discriminated from Ignorance
and from Illusion: these, however, along with
Arbitrary Assumption, afford the most frequent
occasions of error. '^
This paragraph consists of two parts, and these I Expiiea-
shall successively consider. The first is — ' Error is
o Twesteu, Die Lofjik, tniesondcre Ruiz, Cominentarius cle Scieiitia, &c.
die Analutik,%% 308,^09. Ed. [Cf. Disp. xcii. p. 925.]
76 LECTURES ON LOGIC.
LECT. opposed to truth; and Error arises, 1°, From the
^-1 1 commutation of what is subjective with what is ob-
jective in thought ; 2°, From the contradiction of a
supposed knowledge with its laws ; or, 3°, From a
want of adequate activity in our cognitive faculties.'
Error,— " In thc first placc, we have seen that Truth is the
agreement of a thought with its object. Now, as
Error is the opposite of truth, — Error must necessarily
consist in a want of this aoreement. In the second
place, it has been shown, that the criterion or stand-
ard of truth is the necessity founded on the laws of
our cognitive faculties ; and from this it follows that
the essential character of error must be, either that it
is not founded on these laws, or that it is repugnant to
them. But these two alternatives may be viewed as
only one ; for inasmuch as, in the former case, the
judgment remains undecided, and can make no pre-
tence to certainty, it may be thrown out of ac-
count no less than in the latter, where, as positively
contradictory of the laws of knowledge, it is neces-
As Material, sarily false. Of these statements the first, that is, the
non-agreement of a notion with its object, is error
viewed on its material side ; and as a notion is the
common product, — the joint result, afforded by the
reciprocal action of object and subject, it is evident
that whatever the notion contains not correspondent
to the object, must be a contribution by the thinking
subject alone, and we are thus warranted in saying
that Material Error consists in the commuting of
what is subjective with what is objective in thought ;
in other words, in mistaking an ideal illusion for a
As Formal, real representation. The second of these statements
that is, the incongruence of the supposed cognition
with the laws of knowledge, is error viewed on its
LECTURES ON LOGIC. 77
formal side. Now liere the question at once presents lect.
XXVIII.
itself, — How can an act of cognition contradict its
own laws 1 Tlie answer is that it cannot ; and error, Arises from
, , , , • • T ' n 1 1 1 the want of
when more closely scrutinised, is lound not so much adequate
1 1 T j_ • • r ' activity of
to consist m the contradictory activity oi our cogm- the Cogni-
tive faculties as in their want of activity. And this ties,
may be in consequence of one or other of two causes.
For it may arise from some other mental power, — the
will, for example, superseding, — taking the place of,
the defective cognition, or, by its intenser force, turn-
ing it aside and leading it to a false result ; or it may
arise from some want of relative perfection in the ob-
ject, so that the cognitive faculty is not determined by
it to the requisite degree of action.
" What is actually thought, cannot but be correctly
thought. Error first commences when thiuking is re-
mitted, and can in fact only gain admission in virtue
of the truth which it contains ; — every error is a per-
verted truth. Hence Des Cartes " is justified in the
establishment of the principle, — that we would never
admit the false for the true, if we would only give
assent to what we clearly and distinctly apprehend. —
' Nihil nos unquam falsum pro vero admissuros, si
tantum iis assensum pr?ebeamus, quse clare et dis-
tincte percipimus.'" /^ In this view the saying of the
Roman poet : —
" Xam neqiie decipitur ratio, nee decipit iinquam," 7
— is no longer a paradox ; for the condition of error
is not the activity of intelligence, but its inactivity.
So much for the first part of the paragraph. The Error dis-
,. -,-, . ,,... -, f, -f criminated
second is — Jiirror is to be discriminated irom Ignor- from ignor-
a Prlncipia Philosophlce, i. 43. Cf. /3 Twesten, Logik, § 308. — Ed.
Med. iv. De Vero et Falso. y Mauilius, ii. 131. — Ed.
78' LECTURES ON LOGIC.
LECT. ance and from Illusion, which, however, along with
1 Arbitrary Assumption, afford the usual occasions of
ance and -n j
niusion. Jiirror.
Ignorance. " Ignoraucc is a mere negation, — a mere not-know-
ledge ; whereas in error there lies a positive pretence
to knowledge. Hence a representation, be it imper-
fect, be it even without any correspondent objective
reality, is not in itself an error. The imagination of
a hippogriff is not in itself false ; the Orlando Furioso
is not a tissue of errors. Error only arises when we
attribute to the creations of our minds some real
object, by an assertory judgment; w^e do not err and
deceive either ourselves or others, when we hold and
enounce a subjective or problematic supposition only
for what it is. Ignorance, — not-knowledge, — however,
leads to error, when we either regard the unknown as
non-existent, or when we falsely fill it up. The latter
is, however, as much the result of Will, of arbitrary
assumption, as of ignorance; and, frequently, it is the
result of both together. In general, the will has no
inconsiderable share in the activity b}?" which know-
ledge is realised. The will has not immediately an
influence on our judgment, but mediately it has.
Attention is an act of volition, and attention fur-
nishes to the Understanding the elements of its deci-
sion. The will determines whether we shall carry on
our investigations, or break them off, content with the
first apparent probability ; and whether we shall apply
our observations to all, or, only partially, to certain,
momenta of determination.
Illusion. " The occasions of Error which lie in those qualities
of Presentation, Representation, and Thought arising
from the conditions and influences of the thinking
LECTURES ON LOGIC. 'TO
subject itself, are called Illusions. But the existence lect.
of illusion does not necessarily imply the existence of ^^^'
error. Illusion becomes error only when we attribute
to it objective truth ; whereas illusion is no error
when we regard the fallacious appearance as a mere
subjective affection. In the jaundice, we see every-
thing tinged with yellow, in consequence of the suf-
fusion of the eye with bile. In this case, the yellow
vision is illusion ; and it would become error, were
we to suppose that the objects we perceive were really
so coloured. All the powers which co-operate to the its sources.
formation of our judgments, may become the sources
of illusion, and, consequently, the occasions of error.
The Senses,* the Presentative Faculties, External and
Internal, the Eepresentative, the Retentive, the Repro-
ductive, and the Elaborative, Faculties, are immediate,
the Feelings and the Desires are mediate, sources of
illusion. To these must be added the Faculty of
Signs, in all its actual manifestations in language.
Hence we speak of sensible, psychological, moral, and
symbolical, illusion."/^ In all these relations the causes
of illusion are partly general, partly particular ; and
though they proximately manifest themselves in some
one or other of these forms, they may ultimately be
found contained in the circumstances by which the
mental character of the individual is conformed.
Taking, therefore, a general view of all the possible
a La Fontaine. See Mazui-e, Cours alites de la science aux apparences
de Plillosophle, ii. 241. [Toutes les factices que nos sens nous suggerent.
sciences naturelles ne sont autre C'est ce que La Fontaine a tr6s bien
chose qu'une guerre -ouverte de la- exprime dans les vers suivant :
raison coutre les deceptions de la " Quand I'eau courbe un baton, ma
seusibilite c'est-a-dire, qu'elles raison le redresse," &c.^Ed.
ont pour objet de reformer les erreurs /3 [Twesten, Logik, § 309, p. 288-
de nos sens, et de substituer les re- 289, Cf. Sigwart, Lo'jik, §§ 484, 485.]
80
LECTURES ON LOGIC.
LECT,
XXVIII.
Bacon's
classifica-
Sources of Error, I think they may be reduced to the
following classes, which, as they constitute the heads
and determine the order of the ensuing discussion, I
shall comprise in the following paragraph, with which
commences the consideration of the Second Chapter of
Modified Logic. Before, however, proceeding to coii-
ti'oroTtihe sider these several classes in their order, 1 may observe
error. that Bacou is the first philosopher who attempted a
systematic enumeration of the various sources of error; ""
and his quaint classification of these, under the signi-
ficant name of idols, into the four genera of Idols of
the Tribe {idola trihiis). Idols of the Den, [idola specus),
Idols of the Forum {idola fori), which may mean
either the marketplace, the bar, or the place of public
assembly, and Idols of the Theatre, {idola theatri), he
thus briefly characterises.
Par. XCII.
Error, — its
H XCII. The Causes and Occasions of Error
are comprehended in one or other of the four
following classes. For they are found either,
1°, In the General Circumstances which modify
the intellectual character of the individual ; or,
2°, In the Constitution, Habits, and Eeciprocal
Relations of his powers of Cognition, Feeling,
and Desire ; or, 3°, In the Language which he
employs, as an Instrument of Thought and a
Medium of Communication ; or, 4°, In the nature
of the Objects themselves, about which his know-
ledge is conversant.
Par.XCIII.
I. General
circumstan-
ces which
IT XCIII. Under the General Circumstances
which modify the character of the individual, are
o NovKin Or(janum, i. Aph. xxxix. — Ed.
LECTURES ON LOGIC. 81
comprehended 1°. The particular degree of Culti- lect.
vation to which his nation has attained ; for its -1 '.
rudeness, the partiality of its civilisation, and its ^aJ^^Jte?^
over-refinement are all manifold occasions of°[j^^j'°'^'"
error ; and this cultivation is expressed not
merely in the state of the arts and sciences, but
in the degree of its religious, political, and social
advancement ; 2°. The Stricter Associations, in so
far as these tend to limit the freedom of thought,
and to give it a one-sided direction : such are
Schools, Sects, Orders, Exclusive Societies, Cor-
porations, Castes, &c. — "
In the commencement of the Course, I had occasion ExpHca-
to allude to the tendency there is in man to assimilate Man by
in opinions and habits of thought to those with whom social, and
he lives.'^ Man is by nature, not merely by acciden- by the
tal necessity, a social being. For only in society does his feiiows.
he find the conditions which his difierent faculties
require for their due development and application.
But society, in all its forms and degrees, from a family
to a State, is only possible under the condition of a
certain harmony of sentiment among its members ;
and as man is by nature destined to a social existence,
he is by nature determined to that analogy of thouglit
and feeling which society supposes, and out of which
society springs. There is thus in every association,
great and small, a certain gravitation of opinions
towards a common centre. As in our natural body
every part has a necessary sympathy with every
other, and all together form, by their harmonious
conspiration, a healthy whole ; so, in the social body,
o Bacbmann, Logilc, §§ 402, 403.— )3 See Lectures on Metaphysics, vol.
Ed. i. p. 48.— Ed.
VOL. IL F
82 LECTURES ON LOGIC.
LECT. there is always a strong predisposition in each of its
11 '. members to act and think in unison with the rest.
This universal sympathy or fellow-feeling is the prin-
ciple of the different S23irit dominant in different ages,
countries, ranks, sexes, and periods of life. It is the
cause why fashions, why political and religious en-
thusiasm, why moral example either for good or evil,
spread so rapidly and exert so powerful an influence.
As men are naturally prone to imitate others, they,
consequently, regard as important or insignificant, as
honourable or disgraceful, as true or false, as good or
bad, what those around them consider in the same
light."
Pascal Of the various testimonies I formerly quoted, ol
quoted on . ., . . ^ „ -■
the power the stroug assimilatiug influence oi man on man, and
of the power of custom to make that appear true,
natural, and necessary, which in reality is false, un-
natural, and only accidentally suitable, I shall only
adduce that of Pascal, " In the just and the unjust,"
says he, " we find hardly anything which does not
change its character in changing its climate. Three
degrees of an elevation of the pole reverses the whole of
jurisprudence. A meridian is decisive of truth, and a
few years, of possession. Fundamental laws change.
Right has its epochs. A pleasant justice which a river
or a mountain limits ! Truth on this side the Pyre-
nees, error on the other ! "'^ It is the remark of an in-
genious philosopher, " that if we take a survey of the
universe, all nations will be found admiring only the
reflection of their own qualities, and contemning in
of custom.
a. [Wcmers, Unters'urhungen iiher die (vol. ii. p. 126, ed. Faugere.) Com-
Denhkriifte unci Willenslcrdfte clcs pare Lectures on Metaphysics, vol. i,
M enschen, ii. Z22.] p. 86.— Ed.
^ Pensces, partie i. art. vi, § 8,
I
LECTURES ON LOGIC. 83
others whatever is contrary to what they are acciis- lect.
. XXVIIL
tomed to meet with am on 2; themselves. Here is the — 1
EngUshman accusing the French of frivolity ; and
here the Frenchman reproaching the Englishman with
selfishness and brutality. Here is the Arab persuaded
of the infallibility of his Caliph, and deriding the
Tartar who believes in the immortality of the Grand
Lama. In every nation we find the same congratula-
tion of their own wisdom, and the same contempt of
that of their neio;hbours.
" Were there a sage sent down to earth from heaven,
who regulated his conduct by the dictates of pure rea-
son alone, this sage would be universally regarded as
a fool. He would be, as Socrates says, like a physi-
cian accused by the pastry-cooks, before a tribunal of
children, of prohibiting the eating of tarts and cheese-
cakes ; a crime undoubtedly of the highest magnitude
in the eyes of his judges. In vain would this sage
support his opinions by the clearest arguments, — the
most irrefragable demonstrations ; the whole world
would be for him like the nation of hunchbacks,
among whom, as the Indian fabulists relate, there
once u23on a time appeared a god, young, beautiful,
and of consummate symmetry. This god, they add,
entered the capital ; he was there forthwith sur-
rounded by a crowd of natives ; his figure appeared
to them extraordinary ; laughter, hooting, and taunts
manifested their astonishment, and they were about
to carry their outrages still further ; had not one of
the inhabitants (who had undoubtedly seen other
men), in order to snatch him from the danger, sud-
denly cried out — ' My friends ! my friends ! What
are we going to do 1 Let us not insult this miserable
monstrosity. If heaven has bestowed on us the gene-
84 LECTURES ON LOGIC.
LECT. ral gift of beauty, — if it has adorned our backs with
1 '. a mount of flesh, let us with pious gratitude repair to
the temple and render our acknowledgment to the
immortal gods." This fable is the history of human
vanity. Every nation admires its own defects,
and contemns the opposite qualities in its neighbours.
To succeed in a country one must be a bearer of
the national hump of the people among whom he
sojourns.
The art of Thcrc are few philosophers who undertake to make
wdi diffi- their countrymen aware of the ridiculous figure they
cult to teach i*j1 i? ij_*ni? j1 j_'
and to learn, cut lu the ejQ 01 rcasou ; and still lewer the nations
who are able to profit by the advice. All are so punc-
tiliously attached to the interests of their vanity, that
none obtain in any country the name of wise, except
those who are fools of the common folly. There is no
opinion too absurd not to find nations ready to believe
it, and individuals prompt to be its executioners or its
martyrs. Hence it is that the philosopher declared,
that if he held all truths shut up within his hand, he
would take especial care not to show them to his
fellow-men. In fact, if the discovery of a single
truth dragged Galileo to the prison, to what punish-
ment would he not be doomed who should discover
all 1 Among those who now ridicule the folly of the
human intellect, and are indignant at the persecution
of Galileo, there are few who would not, in the age of
that philosopher, have clamoured for his death. They
would then have been imbued with different opinions ;
and opinions not more passively adopted than those
which they at present vaunt as liberal and enlight-
ened. To learn to doubt of our opinions, it is suffi-
cient to examine the powers of the human intellect,
to survey the circumstances by which it is affected.
LECTURES ON LOGIC. 85
and to study the history of human follies. Yet in lect.
. . XXVIII
modern Europe six centuries elapsed from the foun- — 1
dation of Universities until the appearance of that
extraordinary man, — I mean Descartes, — whom his
age first persecuted, and then almost worshipped as a
demi-god, for initiating men in the art of doubting, —
of doubting well,- — a lesson at which, however, both
their scepticism and credulity show that, after two
centuries, they are still but awkward scholars. Socrates
was wont to say — " All that I know is that I know
nothing." " In our age it would seem that men know
everything except what Socrates knew. Our errors
would not be so frequent were we less ignorant ; and
our ignorance more curable, did we not believe our-
selves to be all-wise.
Thus it is that the influence of Society, both in
its general form of a State or Nation, and in its par-
ticular forms of Schools, Sects, &c., determines a
multitude of opinions in its members, which, as they
are passively received, so they are often altogether
erroneous.
Among the more general and influential of these Two genera
there are two, which, though apparently contrary, are, influence of
however, both, in reality, founded on the same in- L^prefudice
capacity of independent thought, — on the same influ- |he oidT **
ence of example, — I mean the excessive admiration of
the Old, and the excessive admiration of the New.
The former of these prejudices,/^ — under which may be
reduced the prejudice in favour of Authority, — was at
a Plato, Apol., p. 23. — Ed. Errcurs et des Prejages repandus dans
fi [On Prejudice in general see the la Soclete, Paris, 1810-1813, 3 vols,
following works : — Dumarsais, Essai 8vo. J. L. Castillon, Essai sur les
sur les Prejuges, new ed., Paris, 1822. Erreurs et les superstitions Anciennes
Examen de V Essai sur les Prejuges, ei iV/oc^erwes, Amsterdam, 1765; Paris,
Berl. 1777. Essai sur les Prejuges, 1767. Sir Thomas Brown, Vulgar
Neuchiitel, 1796. J. B. Sulques, Des Errors, Glanvil, Essmjs.]
86 LECTURES ON LOGIC.
LECT. one time prevalent to an extent of which it is difficult
LI 1 for us to form a conception. This prejudice is pre-
Prepared by pared bj the vcrj education not only which we do,
but which we all must, receive. The child necessarily
learns everything at first on credit, — he believes upon
authority. But when the rule of authority is once
established, the habit of passive acquiescence and
belief is formed, and, once formed, it is not again
always easily thrown off. When the child has grown
up to an age in which he might employ his own reason,
he has acquired a large stock of ideas ; but who can
calculate the number of errors which this stock con-
tains '? and by what means is he able to discriminate
the true from the false 1 Ilis mind has been formed
to obedience and uninquiry ; he possesses no criterion
by which to judge ; it is painful to suspect what has
been long venerated, and it is felt even as a kind of
personal mutilation to tear up what has become irra-
dicated in his intellectual and moral being. Ponere
difficile est quce ])lacuere diu. The adult does not,
therefore, often judge for himself more than the child;
and the tyranny of authority and foregone opinion
continues to exert a sway during the whole course of
his life. In our infancy and childhood the credit
accorded to our parents and instructors is implicit ;
and if what we have learned from them be confirmed
by what we hear from others, the opinions thus re-
commended become at length stamped in almost in-
delible characters upon the mind. This is the cause
why men so rarely abandon the opinions which vul-
garly pass current ; and why what comes as new is
by so many, for its very novelty, rejected as false.
And hence it is, as already noticed, that truth is as it
were geographically and politically distributed ; what
LECTURES ON LOGIC. 87
is truth on one side of a boundary beino; error and lect.
absurdity on the other. What has now been said of — '.
the influence of society at large, is true also of the
lesser societies which it contains, all of which impose
with a stronger or feebler, — a wider or more contracted,
authority, certain received opinions upon the faith of
the members. Hence it is that whatever has once
obtained a recognition in any society, large or small,
is not rejected when the reasons on which it was
originally admitted, have been proved erroneous. It
continues, even for the reason that it is old and has
been accepted, to be accepted still ; and the title which
was originally defective, becomes valid by continu-
ance and prescription.
But opposed to this cause of error, from the preju- 2. Prejudice
dice in favour of the Old, there is the other, directly the New.
the reverse, — the prejudice in favour of the New.
This prejudice may be, in part at least, the result of
sympathy and fellow-feeling. This is the cause why
new opinions, however erroneous, if they once obtain
a certain number of converts, often spread with a
rapidity and to an extent which, after their futility
has been ultimately showD, can only be explained on
the principle of a kind of intellectual contagion. But
the principal cause of the prejudice in favour of
novelty lies in the Passions, and the consideration of
these does not belong to the class of causes with
which we are at present occupied.
Connected with and composed of both these preju- Prejudice
dices, — that in favour of the old and that in favour of Authority,
the new, — there is the prejudice of Learned Authority;
for this is usually associated with the prejudices of
Schools and Sects. " As often as men have appeared,
who, by the force of their genius, have opened up new
88 LECTURES ON LOGIC.
LECT. views of science, and thus contributed to the progress
1 of the human intellect, so often have they, likewise,
afforded the occasion of checking its advancement,
and of turning it from the straight path of improve-
ment. Not that this result is to be imputed as a re-
proach to them, but simply because it is of the nature
of man to be so affected. The views which influenced
these men of genius, and which, consequently, lie at
the foundation of their works, are rarely comprehended
in their totality by those who have the names of these
authors most frequently in their mouths. The many
do not concern themselves to seize the ideal which a
philosopher contemplated, and of which his actual
works are only the imperfect representations ; they
appropriate to themselves only some of his detached
apophthegms and propositions, and of these compound,
as they best can, a sort of system suited to their un-
derstanding, and which they employ as a talisman in
their controversies with others. As their reason is
thus a captive to authority, and, therefore, unable to
exert its native freedom, they, consequently, catch up
the true and the false without discrimination, and
remain always at the point of progress where they
had been placed by their leaders. In their hands a
system of living truths becomes a mere petrified or-
ganism ; and they require that the whole science shall
become as dead and as cold as their own idol. Such
was Plato's doctrine in the hands of the Platonists ;
such was Aristotle's philosophy in the hands of the
Schoolmen ; and the history of modern systems affords
equally the same result.'"*
So much for the first genus into which the Sources
of Error are divided.
« Bachraann, Logik, § 404, p. 550. — Ed,
LECTURES ON LOGIC. 89
LECTUEE XXIX.
MODIFIED STOICHEIOLOGY.
SECTION II. — ERROR ITS CAUSES AND REMEDIES.
A. — GENERAL CIRCUMSTANCES — SOCIETY.
B, — AS IN POWERS OF COGNITION, FEELING, AND
DESIRE.
I. AFFECTIONS. PRECIPITANCY — SLOTH HOPE AND
FEAR — SELF-LOVE.
In our last Lecture, we entered on the consideration lect.
XXIX
of the various sources of Error. These, I stated,
may be conveniently reduced to four heads, and con- ^^n!^'*^*"
sist, 1°. In the General Circumstances which modify
the intellectual character of the individual ; 2°. In the
Constitution, Habits, and Eeciprocal Eelations of his
powers of Cognition, Feeling, and Desire ; 3°. In the
Language which he employs as an Instrument of
Thought and a Medium of Communication ; and 4°. In
the nature of the Objects themselves about which his
knowledge is conversant.
Of these, I then gave you a general view of the
nature of those occasions of Error, which originate in
the circumstances under the influence of which the
character and opinions of man are determined for
him as a member of society. Under this head I
90 LECTURES ON LOGIC.
LECT. stated, tliat, as man is destined by liis Creator to fulfil
XXIX . • •
L the end of his existence in society, he is wisely fur-
nished with a disposition to imitate those among
whom his lot is cast, and thus to conform himself to
whatever section of human society he may by birth
belong, or of which he may afterwards become a
member. The education we receive, nay the very
possibility of receiving education at all, supposes to a
certain extent the passive infusion of foreign and tra-
ditionary opinions. For as man is compelled to think
much earlier than he is able to think for himself, — all
education necessarily imposes on him many opinions
which, whether in themselves true or false, are, in re-
ference to the recipient, only prejudices ; and it is
even only a small number of mankind, who at a later
period are able to bring these obtruded opinions to
the test of reason, and by a free exercise of their own
intelligence to reject them if found false, or to acknow-
ledge them if proved true.
But while the mass of mankind thus remain, during
their whole lives, only the creatures of the accidental
circumstances which have concurred to form for them
their habits and beliefs; the few who, are at last able
to form opinions for themselves, are still dependent,
in a great measure, on the unreasoning judgment
of the many. Public opinion, hereditary custom,
despotically impose on us the capricious laws of pro-
priety and manners. The individual may possibly, in
matters of science, emancipate himself from their ser-
vitude ; in the affairs of life he must quietly submit
himself to the yoke. The only freedom lie can here
prudently manifest, is to resign himself with a con-
sciousness that he is a slave not to reason but to con-
I
LECTURES ON LOGIC. 91
ventional accident. And while he conforms himself lect.
XXIX
to the usages of his own society, he will be tolerant -
to those of others. In this respect his maxim will be
that of the Scythian prince : — " AVith you such may
be the custom, — with us it is different."
So much for the general nature of the influence to Means by
which we are exposed from the circumstances of So- influence of
111 society, as a
ciety; it now remains to say what are the means by source of
which this influence, as a source of error, may be be co'unter-
- acted.
counteracted.
It has been seen that, in consequence of the man- Necessary
-, . ^ • • /. 1 r 1 J.1 to institute
ner m which our opinions are lormed lor us by tne a critical
. T , p . , . T T -11 examination
accidents ol society, our imposed and supposed know- of the con-
ledge is a confused medley of truths and errors. knowLdge!
Here it is evidently necessary to institute a critical
examination of the contents of this knowledge. Des-
cartes proposes that, in order to discriminate, among
our prejudiced opinions, the truths from the errors, we
ought to commence by doubting all." This has ex-
posed him to much obloquy and clamour ; but most
unjustly. The doctrine of Descartes has nothing Descartes,
sceptical or offensive ; for he only maintains that it cept? '"^'^
behoves us to examine all that has been inculcated on
us from infancy, and under the masters to whose
authority we have been subjected, with the same at-
tention and circumspection which we accord to dubi-
ous questions. In fact there is nothing in the precept
of Descartes, which had not been previously enjoined
by other philosophers. Of these I formerly quoted to
you several, and among others the remarkable testi-
monies of Aristotle, St Augustin, and Lord Bacon./^
« Biscours de la Methode, Partie /3 See Lectures on Metaphysics, vol
ii.— Ed. i. p. 90 et seq. — Ed.
92 LECTURES ON LOGIC.
LECT. But altliough there be notliiDg reprehensible in the
. L precept of Descartes, as enounced by him, it is of
Conditions less practical utility in consequence of no account
dify i\s''"'" being taken of the circumstances which condition and
application, ^^j-f^ '^g application. For, in the first place, the
judgments to be examined ought not to be taken at
random, but selected on a principle, and arranged in
due order and dependence. But this requires no
ordinary ability, and the distribution of things into
their proper classes is one of the last and most diffi-
cult fruits of philosophy. In the second place, there
are among our prejudices, or pretended cognitions,
a great many hasty conclusions, the investigation of
which requires much profound thought, skill, and ac-
quired knowledge. Now, from both of these consider-
ations, it is evident that to commence philosophy by
such a review, it is necessary for a man to be a philo-
sopher before he can attempt to become one. The
precept of Descartes is, therefore, either unreasonable,
or it is too unconditionally expressed. And this latter
alternative is true.
A gradual What cau bc rationally required of the student of
andprogres- ^ _ . .
8ive abroga- phllosophy, Is uot a preliminary and absolute, but a
judiccsaii gradual and progressive abrogation, of preiudices. It
that can be ° ^ ^. , ^ .
required of cau ouly bc rcqulrcd of him, that, when, in the course
ofphiio- of his study of philosophy, he meets with a proposi-
tion which has not been already sufficiently sifted, —
(whether it has been elaborated as a principle or ad-
mitted as a conclusion), — he should pause, discuss it
without prepossession, and lay aside for future con-
sideration all that has not been subjected to a search-
ing scrutiny. The precept of Descartes, when rightly
explained, corresponds to that of St Paul " : " If any
o 1 Cor., iii. 18.
LECTURES ON LOGIC. 93
man amona; you seemetli to be wise in this world, let lect.
. . XXIX.
liim become a fool, that he may be wise ; " that is, let '-
him not rely more on the opinions in which he has
been brought up, and in favour of which he and those
around him are prejudiced, than on so many visions
of imagination ; and let him examine them with the
same circumspection as if he were assured that they
contain some truth among much falsehood and many
extravagancies,"
Proceedina: now to the second class of the Sources
of Error, which are found in the Mind itself, I shall
commence with the following paragraph : —
IF XCIV. The Sources of Error which arise Par. xciv.
from the Constitution, Habits, and reciprocal of Error
-i-» o 1 c r^ • • T\ T arising from
Eelations of the powers of Cognition, Jb eelmg, the powers
and Desire, may be subdivided into two kinds, tion, Feei-
f> 1 • • 1 1 '"^S; and
The first of these consists in the undue prepon- Desire,— of
derance of the Affective Elements of mind, (the
Desires and Feelings), over the Cognitive : the
second, in the weakness or inordinate strength
of some one or other of the Cognitive Faculties
themselves.
Afiection is that state of mind in which the Feel- Expiica-
ings and Desires exert an influence not under the con- 1. Prcpon-
trol of reason ; in other words, a tendency by which Affection
the intellect is impeded m its endeavour to think an nition.
object as that object really is, and compelled to think
it in conformity with some view prescribed by the
passion or private interest of the subject thinking.
a This criticism of the precept of taken from Crousaz, Locjique, t. iiL
Descartes is, with some slight changes, part ii., ch. 6, p. 263 et seq. — Ed.
9i LECTUEES ON LOGIC.
LECT. The human mind, when unruffled by passion, may
L be compared to a calm sea. A calm sea is a clear
mirror, in which the sun and clouds, in which the
Influence of forms of heavcu and earth, are reflected back pre-
tife Mbr cisely as they are presented. But let a wind arise ;
and the smooth clear surface of the water is lifted
into billows and agitated into foam. It no more re-
flects the sun and clouds, the forms of heaven and
earth, or it reflects them only as distorted and broken
images. In like manner, the tranquil mind receives
and reflects the world without as it truly is ; but let
the wind of passion blow, and every object is repre-
sented, not as it exists, but in the colours and aspects
and partial phases in which it pleases the subject to
regard it. The state of passion and its influence
Boethius on the Cognitive Faculties are truly pictured by
''"''''• Boethius.'^
" Nubibus atris
Condita nullum Tu quoque si vis
Fuudere possunt Lumine claro
Sidera lumen. Cernere verum,
Si mare volvens Tramite recto
Turbidus auster Carpere callem :
Misceat sestum, Gaudia pelle,
Vitrea dudum, Pelle timorem.
Parque serenis Spemque fugato,
Unda diebus, Nee dolor adsit,
Mox resoluto Nubila mens est,
Sordida coeno, Viuctaque frenis,
Visibus obstat. Hsec ubi regnant."
Error Evcry error consists in this, — that we take some-
limited to , . „ . . , ,
Provable thiug lor non-cxistcnt, because we have not become
Reasoning.
aware of its existence, and that, in place of this ex-
a De ConsoL Phil, L. i., Metr. 7.— Ed.
LECTURES ON LOGIC. 95
istent something, we fill up the premises ot a probable lect.
reasoning with somethiuo; else.
I have here limited the possibility of error to Pro-
bable Reasoning, for, in Intuition and Demonstration,
there is but little possibility of important error.
Hobbes indeed asserts that had it been contrary to the
interest of those in authority, that the three angles of
a triangle should be equal to two right angles, this
truth would have been long ago proscribed as heresy,
or as high treason." This may be an ingenious illus-
tration of the blind tendency of the passions to sub-
jugate intelligence ; but we should take it for more
than was intended by its author, were we to take it
as more than an ingenious exaggeration. Limiting,
therefore, error to probable inference, (and this consti-
tutes, with the exception of a comparatively small
department, the whole domain of human reasoning),
we have to inquire, How do the Passions influence us
to the assumption of false premises ? To estimate the
amount of probability for or against a given propo-
sition, requires a tranquil, an unbiassed, a comprehen-
sive, consideration, in order to take all the relative
elements of judgment into due account. But this
requisite state of mind is disturbed when any interest,
any wish, is allowed to interfere.
^ XCV. The disturbing Passions may be re- Par. xcv.
duced to four : — Precipitancy, Sloth, Hope and sions, as
sources of
Fear, Self-love. Error,—
o ' n -y ' ' t reduced to
1 . A restless anxiety for a decision begets four.
impatience, which decides before the preliminary
inquiry is concluded. This is Precipitancy.
a Leviathan, Pai't I. ch. 11. — Ed.
96 LECTUKES ON LOGIC.
LECT. 2°. The same result is the effect of Sloth,
XXIX • • •
L which dreams on in conformity to custom, with-
out subjecting its beliefs to the test of active
observation.
3°. The restlessness of Hope or Fear impedes
observation, distracts attention, or forces it only
on what interests the passion ; — the sanguine
looking only on what harmonises with his hopes,
the diffident only on what accords with his
fears.
4°. Self-love perverts our estimate of proba-
bility by causing us to rate the grounds of judg-
^ ment, not according to their real influence on the
truth of the decision, but according to their
bearing on our personal interests therein.
Expiica- In regard to Impatience or Precipitation, — "all is
i.^Precipi- the cause of this which determines our choice on one
*'^'"^^' side rather than another. An imagination excites
pleasure, and because it excites pleasure we yield our-
selves up to it. We suppose, for example, that we
are all that we ought to be, and why '? Because this
supposition gives us pleasure. This, in some disposi-
tions, is one of the greatest obstacles to improvement ;
for he who entertains it, thinks there is no necessity to
labour in order to become what he is already. ' I be-
Seneca. licvc,' says Scueca," ' that many had it in their power
to have attained to wisdom, had they not been im-
peded by the belief that wisdom they had already
attained.' ' Multos puto ad sapientiam potuisse per-
Erasmus. vcuire, uisl putasscut sc pervenissc.'" ^ Erasmus gives
a De Tranquillitate Animi, c. 1.— $ Crousaz, Logique, t. iii., part. ii.
Ed. ch. 7, p. 297.— Ed.
LECTURES ON LOGIC. 97
the following as tlie principal advice to a young lect,
votary of learning in the conduct of his studies : " To — '
read the most learned books, to converse with the
most learned men ; but, above all, never to conceit
that he himself was learned." "
" From the same cause, men flatter themselves with iiiustra-
the hope of dying old, although few attain to longe-
vity. The less probable the event the more certain
are they of its occurrence ; and why 1 Because the im-
agination of it is agreeable. ' Decrepiti senes pauco- From
, . T ■ , • Seneca.
rum annorum accessionem votis mendicant ; mmores
natu seipsos esse fingunt : mendacio sibi blandiuntur:
et tam libenter fallunt, quam si fata una decipiant.' " ^
" Preachers," says Montaigne, " are aware that the From
emotion which arises during their sermons animates °^ '^'^
themselves to belief, and we are conscious that when
roused to anger we apply ourselves more intently to
the defence of our thesis, and embrace it with greater
vehemence and approbation, than we did when our
mind was cool and unruffled. You simply state your
case to an advocate ; he replies w^ith hesitation and
doubt : you are aware that it is indifferent to him
whether he undertakes the defence of the one side or of
the other ; but have you once fee'd him well to take
your case in hand ; he begins to feel an interest in it,
his will is animated. His reason and his science be-
come also animated in proportion. Your case presents
itself to his understandino; as a manifest and indubit-
able truth ; he now sees it in a wholly different light,
a " Joannes Alexander Brassicanus se doctum nunquam piitaret." Motto
rogavit Erasmum, qua ratione doctus to G. J. Vossius, Opuscula de Studi-
posset fieri, respondit ex tempore : orum Ratione. See Crenius, Consilia
si doctis assidue conviveret, si doctos et Methodus, &c., p. 686, 1692. — Ed.
audiret non minus submisse quam fi Heneca, De Brevitate Fito, c. 11.
honorifice, si doctos strenue legeret, si Crousaz, Logique, t. iii. p. ii. ch. 7, p.
doctos diligenter edisceret, denique si 297, ed. 1725. — Ed.
VOL. TL G
98 LECTUKES ON LOGIC.
LECT. aud really believes that you have law and justice on
XXIX . .
'- your side." " It is proper to observe that Montaigne
was himself a lawyer, — he had been a counsellor of the
Parliament of Bordeaux.
Precipitate It might scem that Precipitate Dogmatism and an
anTETeptu inclination to Scepticism were opposite characters of
o'/Kame^ mlud. They are, however, closely allied, if not merely
isposi ion. pj^^ggg q£ ^j^g same disposition. This is indeed con-
fessed by the sceptic Montaigne.^ "The most un-
easy condition for me is to be kept in suspense on
urgent occasions, and to be agitated between fear
and hope. Deliberation, even in things of lightest
moment, is very troublesome to me ; and I find
my mind more put to it, to undergo the various
tumbling and tossing of doubt and consultation,
than to set up its rest, and to acquiesce in whatever
shall happen, after the die is thrown. Few passions
break my sleep ; but of deliberations, the least dis-
turbs me."
Remedy Prccipitatiou is no incurable disease. There is for
tation.^"^' it one sure and simple remedy, if properly applied.
It is only required, to speak with Confucius, manfully
to restrain the wild horse of precipitancy by the curb
of consideration, — to weigh the reasons of decision,
each and all, in the balance of cool investigation, — not
to allow ourselves to decide until a clear conscious-
ness has declared these reasons to be true, — to be suffi-
cient ; and, finally, to throw out of account the suf-
frages of self-love, of prepossession, of passion, and to
admit only those of reflection, of experience, and of
evidence. This remedy is certain and effectual. In
theory it is satisfactory, but its practical application
a Essais, L. ii. ch. 12. Quoted by ;3 Essais, L. ii. c. 17. — Ed.
Crousaz, l. c. — Ed.
LECTURES ON LOGIC. 99
requires a moral resolution, for the acquisition of lect.
. . XXIX
whicli no precept can be given.
In the second place, "Sloth is likewise a cause of 2. sioth.
precipitation, and it deserves the more attention as it
is a cause of error extremely frequent, and one of
which we are ourselves less aware, and which is less
notorious to others. We feel it fatiguing to continue
an investigation, therefore we do not pursue it ; but
as it is mortifying to think that we have laboured in
vain, we easily admit the flattering illusion that we
have succeeded. By the influence of this disposition
it often happens, that, after having rejected what first
presented itself, — after having rejected a second time
and a third time what subsequently turned up, be-
cause not sufficiently applicable or certain, we get
tired of the investigation, and perhaps put up with
the fourth suggestion, which is not better, haply even
worse, than the preceding ; and this simply because it
has come into the mind when more exhausted and less
scrupulous than it was at the commencement," « " The Senera
volition of that man," says Seneca, " is often frus-
trated, who undertakes not what is easy, but who
wishes what he undertakes to be easy. As often as
you attempt anything, compare together yourself, the
end which you propose, and the means by which it is
to be accomplished. For the repentance of an un-
finished work will make you rash. And here it is of
consequence whether a man be of a fervid or of a
cold, of an aspiring or of a humble, disposition." ^
To remedy this failing it is necessary, in conform- its remedy,
ity with this advice of Seneca, to consult our forces,
and the time we can afibrd, and the difiiculty of the
o Crousaz, Logique, t. iii. part ii. ch. j3 De Ira, L. iii. c. 7. Quoted by
7, p. 302. — Ed. Crousaz, Logique, i. iii. p. 302. — Ed.
100 LECTURES ON LOGIC.
LECT. subjects on wliicli we enter. We ouglit to labour only
'- at intervals, to avoid the tedium and disquiet conse-
quent on unremitted application ; and to adjourn the
consideration of any thought which may please us
vehemently at the moment, until the prepossession in
its favour has subsided with the animation which gave
it birth.
3. Hope The two Causes of premature judgment, — the affec-
tions of Impatience and Sloth, — being considered, I pass
on to the third principle of Passion, by which the in-
tellect is turned aside from the path of truth, — I mean
the disturbing influence of Hope and Fear. These
passions, though reciprocally contrary, determine a
similar effect upon the deliberations of the Under-
standing, and are equally unfavourable for the in-
terest of truth. In forming a just conclusion upon a
question of probable reasoning, that is, where the
grounds of decision are not few, palpable, and of de-
terminate effect, — and such questions may be said to
be those alone on which differences of opinion may
arise, and are, consequently, those alone which re-
quire for their solution any high degree of observation
and ingenuity, — in such questions hope and fear
exert a very strong and a very unfavourable influ-
ence. In these questions it is requisite, in the first
place, to seek out the premises ; and, in the second,
to draw the conclusion. Of these requisites the first
is the more important, and it is also by far the more
difficult.
How Hope Now the passious of Hope and Fear operate sever-
operateun- ally to prcvcut the intellect from discovering all the
on the\Tn- clemcuts of dccisiou, which ought to be considered in
derstanding. p • ■ i • i • i •
lormmg a correct conclusion, and cause it to take into
account those only which harmonise with that con-
LECTURES ON LOGIC. 101
elusion to wliicli tlie actuating passion is inclined, lect.
And here the passion operates in two ways. In the L
first place, it tends so to determine the associations of
thought, that only those media of proof are suggested
or called into consciousness, which support the conclu-
sion to which the passion tends. In the second place,
if the media of proof by which a counter conclusion is
supported, are brought before the mind, still the mind
is influenced by the passion to look on their reality
with doubt, and, if such cannot be questioned, to
undervalue their inferential importance ; whereas it is
moved to admit, without hesitation, those media of
proof, which favour the conclusion in the interest of
our hope or fear, and to exaggerate the cogency with
which they establish this result. Either passion looks
exclusively to a single end, and exclusively to the
means by which that single end is accomplished.
Thus the sanguine temperament, or the mind under
the habitual predominance of hope, sees only and
magnifies all that militates in favour of the wished-
for consummation, which alone it contemplates ;
whereas the melancholic temperament, or the mind
under the habitual predominance of fear, is wholly
occupied with the dreaded issue, views only what
tends to its fulfilment, while it exaggerates the pos-
sible into the probable, the probable into the certain.
Thus it is that whatever conclusion we greatly hope or
greatly fear, to that conclusion we are disposed to
leap ; and it has become almost proverbial, that men
lightly believe both what they wish, and what they
dread, to be true.
But the influence of Hope on our judgments, inclin-
ing us to find whatever we wish to find, in so far as
this arises from the illusion of Self-love, is compre-
102 LECTURES ON LOGIC.
LECT. headed in tliis, — the fourth cause of Error, — to which
XXIX. T 1
1 now proceed.
4. Self-love. Sclf-lovc, uudcr wliich I inckide the dispositions of
Vanity, Pride, and, in general, all those which incline
us to attribute an undue weight to those opinions in
which we feel a personal interest, is by far the most
extensive and influential impediment in the way of
reason and truth. In virtue of this principle, what-
ever is ours, — whatever is adopted or patronised by
us, whatever belongs to those to whom we are at-
tached, — is either gratuitously clothed with a charac-
ter of truth, or its pretensions to be accounted true
are not scrutinised with the requisite rigour and im-
partiality. I am a native of this country, and, there-
fore, not only is its history to me a matter of peculiar
interest, but the actions and character of my country-
men are viewed in a very difierent light from that in
which they are regarded by a foreigner. I am born
and bred a member of a religious sect, and because
they constitute my creed, I find the tenets of this
sect alone in conformity to the Word of God. I am
the partisan of a philosophical doctrine, and am,
therefore, disposed to reject whatever does not har-
monise with my adopted system.
Aristotle,— It Is tlic part of a philosopher, says Aristotle, inas-
' much as he is a philosopher, to subjugate self-love,
and to refute, if contrary to truth, not only the opin-
ions of his friends, but the doctrines which he himself
may have professed." It is certain, however, that
philosophers, — for philosophers are men, — have been
too often found to regulate their conduct by the oppo-
iiiustrations sitc principle. That man pretended to the name of
cnce of Self- philosopher, who scrupled not to declare that he
a Eth. Nic, i. 4 ((!).— Ed.
LECTURES ON LOGIC. 103
would rather be in the wrons: with Plato than in the lect.
. . XXIX
right with his opponents." " Gisbert Voetius urged 1
Mersennus to refute a work of Descartes a year before opinioas.
the book appeared, and before he had himself the
means of judging whether the opinions it contained
were right or wrong. A certain professor of philo-
sopliy in Padua came to Galileo, and requested that he
would explain to him the meaning of the term paral-
laxis ; which he wished, he said, to refute, having
heard that it was opposed to Aristotle's doctrine
touching the relative situation of the comets. What !
answered Galileo, you wish to controvert a word
the meaning of which you do not know I Redi
tells us that a sturdy Peripatetic of his acquaint-
ance would never consent to look at the heavens
through a telescope, lest he should be compelled to
admit the existence of the new stars discovered by
Galileo and others. The same Redi informs us that
he knew another Peripatetic, a staunch advocate of
the Aristotelian doctrine of equivocal generation, (a
doctrine, by the way, which now again divides the
physiologists of Europe), and w^ho, in particular, main-
tained that the green frogs which appear u2:>on a
shower come down with the rain, who would not be
induced himself to select and examine one of these
frogs. And why '? Because he w-as unwilling to be
convicted of his error, by Redi showing him the green
matter in the stomach, and its feculse in the intestines
of the animal."^ The spirit of the Peripatetic
philosophy was, however, wholly misunderstood by
these mistaken followers of Aristotle ; for a true
a Cicero, Tusc. Qucest., i. 17. 1766, § 332. First published in 1756.
/SReimarus, p. 389. [Die Vernunft- The above four anecdotes are all taken
lehre, ron H.S.R. (Hermann Samuel from this work. — Ed.]
lieimarus), dritte Auflnge, Hamburg,
104 LECTURES ON LOGIC.
LECT. Aristotelian is one who listens rather to the voice of
XXIX
^ ' ^ ' nature than to the precept of any master, and it is
well expressed in the motto of the great French anato-
mist, — Eiolanus est Peripateticus ; credit ea, et ea
tantum, quse vidit. From the same principle pro-
ceeds the abuse, and sometimes even the persecution,
which the discoverers of new truths encounter from
those whose cherished opinions these truths subvert.
Self-love In like manner, as we are disposed to maintain our
leads us to , . . , . , 1 • 1 p 1
regard with owu opiuiou, WO arc mchnedto regard with favour the
opinions of opiulous of thoso to whom we are attached by love,
whom we gratitude, and other conciliatory affections. " We do
are in any t • i i f c • i
way attach- uot lunit our attachment to the persons of our friends,
— we love in a certain sort all that belongs to them ;
and as men generally manifest sufficient ardour in
support of their opinions, we are led insensibly by a
kind of sympathy to credit, to approve, and to defend
these also, and that even more passionately than our
friends themselves. We bear affection to others for
various reasons. The agreement of tempers, of inclina-
tions, of pursuits ; their appearance, their manners,
their virtue, the partiality which they have shown to
us, the services we have received at their hands, and
many other particular causes, determine and direct our
love.
Male- " It is observed by the 2;reat Malebranche," that if
branche n n • -i n
adduced to auv of our fiicnds, — any even of those we are disposed
this effect. "^ -^ . . ^
to love, — advance an opinion, w^e forthwith lightly
allow ourselves to be persuaded of its truth. This
opinion we accept and support, without troubling our-
selves to inquire whether it be conformable to fact,
frequently even against our conscience, in conformity
to the darkness and confusion of our intellect, to the
o Recherche clc la Vcrite, L. iv. ch. 13. — Ed.
LECTURES ON LOGIC. 105
corruption of our heart, and to the advantages which lect.
XXIX
we hope to reap from our facility and complaisance."" — ^ — ^
The influence of this principle is seen still more This shown
^^ ^ especially
manifestly when the passion chano-es ; for thous^h the when the
'' -■■ ^ '-' ^ passion
things themselves remain unaltered, our judgments changes,
concerning them are totally reversed. How often do
we behold persons who cannot, or will not, recognise
a single good quality in an individual from the mo-
ment he has chanced to incur their dislike, and who
are even ready to adopt opinions, merely because
opposed to others maintained by the object of their
aversion "? The celebrated Arnauld/^ a;oes so far even Amauki
as to assert, that men are naturally envious and jeal- man is
1 . . . . , ^ 1 naturally
ous ; that it is with pain they endure the contem- envious.
plation of others in the enjoyment of advantages
which they do not themselves possess ; and, as the
knowledge of truth and the power of enlightening
mankind is of one of these, that they have a secret in-
clination to deprive them of that glory. This accord-
ingly often determines them to controvert without a
ground the opinions and discoveries of others. Self-
love accordingly often argues thus : — ' This is an
opinion which I have originated, this is an opinion,
therefore, which is true ; ' whereas the natural
malignity of man not less frequently suggests such
another : ' It is another than I who has advanced this
doctrine ; this doctrine is, therefore, false.'
We may distinguish, however, from malignant or The love of
envious contradiction another passion, which, though tion.
more generous in its nature and not simply a mode of
Self-love, tends, nevertheless, equally to divert us from
the straight road of truth, — I mean Pugnacity, or the
« Caro, Nouvelle Lofj'ique, part ii., ^ VArt de Penser {Port-Royal Lo-
ch, viii., p. 288.— Ed. gic), p. iii. ch. 20 Ed.
106 LECTURES ON LOGIC.
LECT. love of Disputation. Under the influence of tins
^^^ ' passion, we propose as our end victory, not truth.
We insensibly become accustomed to find a reason for
any ojoinion, and, in placing ourselves above all rea-
sons, to surrender our belief to none. Thus it is why
two disputants so rarely ever agree, and why a ques-
tion is seldom or never decided in a discussion, where
the combative dispositions of the reasoners have once
been roused into activity. In controversy it is
always easy to find wherewithal to reply ; the end
of the parties is not to avoid error, but to impose
silence ; and they are less ashamed of continuing
wrong than of confessing that they are not right.'*
These affec- Thcsc affcctions may be said to be tlie immediate
immediate causcs of all crror. Other causes there are, but not
causes of all . t , x n r • i . i 1 1 r
error. immediate. In so lar as Logic detects the sources oi
cond™onr^ our false judgments and shows their remedies, it must
fo^'the ^ carefully inculcate that no precautionary precept for
ofprecejts particular cases can avail, unless the inmost principle
sources o^ of tlic cvil bc discovcrcd, and a cure applied. You
must, therefore, as you would remain free from the
hallucination of false opinion, be convinced of the ab-
solute necessity of following out the investigation of
every question calmly and without passion. You must
learn to pursue, and to estimate, truth without distrac-
tion or bias. To this there is required, as a primary
condition, the unshackled freedom of thought, the
equal glance which can take in the whole sphere of
observation, the cool determination to pursue the
truth whithersoever it may lead ; and, what is still
more important, the disposition to feel an interest in
truth, and in truth alone. If perchance some col-
lateral interest may first prompt us to the inquiry,
aL'Art de Penser, p. iii., ch. 20. ch. 9, p. 311, Paris, 1820.— Ed.
Cf. CarOj Nouvclle Loglquc, part ii.,
error.
LECTURES ON LOGIC. 107
in our general interest for trutli we must repress, — lect.
we must forget, this interest, until the inquiry be con- '.
eluded. Of what account are the most venerated
opinions if they be untrue 1 — At best they are only
venerable delusions. He who allows himself to be
actuated in his scientific procedure by any partial in-
terest, can never obtain a comprehensive survey of the
whole he has to take into account, and always, there-
fore? remains incapable of discriminating, with accu-
racy, error from truth. The independent thinker must,
in all his inquiries, subject himself to the genius of
truth, — must be prepared to follow her footsteps
without faltering or hesitation. In the consciousness
that truth is the noblest of ends, and that he pursues
this end with honesty and devotion, he will dread no
consequences, — ^for he relies upon the truth. Does he
compass the truth, he congratulates himself on his
success ; does he fall short of its attainment, he knows
that even his present failure will ultimately advance
him to the reward he merits. Err he may, and that
perhaps frequently, but he will never deceive himself.
We cannot, indeed, rise superior to our limitary na-
ture, we cannot, therefore, be reproached for failure ;
but we are always responsible for the calmness and
impartiality of our researches, and these alone render
us worthy of success. But though it be manifest,
that to attain the truth we must follow whithersoever
the truth may lead, still men in general are found to
yield not an absolute, but only a restricted, obedience
to the precept. They capitulate, and do not uncon-
ditionally surrender. I give up, but my cherished
dogma in religion must not be canvassed, says one ; —
ray political principles are above inquiry, and must
be exempted, says a second ; — my country is the land
of lands, this cannot be disallowed, cries a third ; —
108
LECTUEES ON LOGIC.
LECT.
XXIX.
my order, my vocation, is undoubtedly the noblest,
exclaim a fourth and fifth ; — only do not require that
we should confess our having erred, is the condition
which many insist on stipulating. Above all, that
resolve of mind is difficult, which is ready to sur-
render all fond convictions, and is prepared to re-
commence investigation the moment that a funda-
mental error in the former system of belief has been
detected. These are the principal grounds why,
among men, opinion is so widely separated from
opinion ; and why the clearest demonstration is so
frequently for a season frustrated of victory.
Par. xcvi.
Rules
against
Errors from
the Affec-
tions.
IT XCVI. Against the Errors which arise from
the Affections, there may be given the three
following rules : —
1°. When the error has arisen from the influ-
ence of an active affection, the decisive judg-
ment is to be annulled ; the mind is then to be
freed, as far as possible, from passion, and the
process of inquiry to be recommenced as soon
as the requisite tranquillity has been restored.
2°. When the error has arisen from a relaxed
enthusiasm for knowledge, we must reanimate
this interest by a vivid representation of the
paramount dignity of truth and of the lofty
destination of our intellectual nature.
3°. In testing the accuracy of our judgments,
we must be particularly suspicious of those
results which accord with our private inclina-
tions and predominant tendencies.
These rules require no comment.
^
LECTURES ON LOGIC. 109
LECTURE XXX.
MODIFIED STOICHEIOLOGY.
SECTION II. — EREOR — ITS CAUSES AND REMEDIES.
B. — AS IN THE COGNITIONS, FEELINGS, AND DESIRES.
II. — WEAKNESS AND DISPROPORTIONED STRENGTH
OF THE FACULTIES OF KNOWLEDGE.
I NOW go on to tlie Second Head of the class of Errors lkct.
founded on the Natural Constitution, the Acquired "'''
Weakness
spr
Habits, and the Reciprocal Relations of our Cognitive anrm
and Affective Powers, that is, to the Causes of Error ^trength^of
which originate in the Weakness or Disproportioned J||!; ^r"''
Strength of one or more of our Faculties of Knowledge knowledge,
themselves.
Here, in the first place, I might consider the errors Neglect of
which have arisen from the Limited Nature of the Naturnf*^'
Human Intellect in general, — or rather from the mis- inteiieTr
takes that have been made by philosophers in denying erroT "
or not taking this limited nature into account." The
illustration of this subject is one which is relative to
a [On this subject see Crusius.] menschlichen Erlcenntniss, § 443, 1st
[Cliristian August Crusius, Weg ziir ed. 1747. — Ed.]
Geivissheit unci ZuverldssigJceit der
110 LECTURES ON LOGIC.
LECT. and supposes an acquaintance with, some of the ab-
— ^ — '— strusest speculations in Philosophy, and which belong
not to Logic, but to Metaphysics, I shall not, therefore,
do more than simply indicate at present, what it will
1. Phiio- be proper at another season fully to explain. It is
Absohuc."" manifest, that, if the human mind be limited, — if it
only knows as it is conscious, and if it be only con-
scious, as it is conscious of contrast and opposition, —
of an ego and non-ego ; — if this supposition, I say, be
correct, it is evident that those philosophers are in
error, who virtually assume that the human mind is
unlimited, that is, that the human mind is capable oi
a knowledge superior to consciousness, — a cognition
in which knowledge and existence,' — the Ego and
non-Ego, — God and the creature, — are identical; that
is, of an act in which the mind is the Absolute, and
knows the Absolute. This philosophy, the statement
of which, as here given, it would require a long com-
mentary to make you understand, is one which has
for many years been that dominant in Germany ; it
is called the Philosophy of the Absolute, or the Phi-
losophy of Absolute Identity. This system, of which
Schelling and Hegel are the great representatives, errs
by denying the limitation of human intelligence with-
out proof, and by boldly building its edifice on this
gratuitous negation."
•2. A one- But thcrc are other forms of philosophy, which err
ofthefinit- not in actually postulating the infinity of mind, but
" in taking only a one-sided view of its finitude. It is
a general fact, which seems, however, to have escaped
the observation of philosophers, that whatever we can
positively compass in thought, — whatever we can con-
a See Discussions, p. 19. — Ed.
LECTURES ON LOGIC. Ill
ceive as possible, — in a word, tlie omne coqitahile, lies lect.
. . XXX
between two extremes or poles, contradictorily op- L
posed, and one of which must, consequently, be true,
but of neither of which repugnant opposites are we
able to represent to our mind the possibility." To niustrated
■1 ^ 1^ e ^^' reference
take one example out oi many : we cannot construe to the two
to the mind as possible the absolute commencement toHes, -the
of time ; but we are equally unable to think the j)os- commence-
sibility of the counter alternative, — its infinite or ab- thrinfiu'^ite
solute non-commencement, in other words, the infinite mracement,
regress of time. Now it is evident, that, if we looked ''
merely at the one of these contradictory opposites and
argued thus : — whatever is inconceivable is impos-
sible, the absolute commencement of time is incon-
ceivable, therefore the absolute commencement ol
time is impossible ; but, on the principles of Contra-
diction and Excluded Middle, one or other of two op-
posite contradictories must be true ; therefore, as the
absolute commencement of time is impossible, the ab-
solute or infinite non-commencement of time is neces-
sary : — I say, it is evident that this reasoning would
be incompetent and one-sided, because it might be
converted ; for, by the same one-sided process, the
opposite conclusion might be drawn in fiivour of the
absolute commencement of time.
Now, the unilateral and incompetent reasoning The same
which I have here supposed in the case of time, is exemlfilLd
one of which the Necessitarian is guilty, in his argu- Ihe Necessl-
ment to prove the impossibility of human volitions mentl^a^St
being free. He correctly lays down, as the founda- V^ihT" "^
tion of his reasoning, two propositions which must at wT
once be allowed : 1°, That the notion of the liberty of
o See Discussions, p. 601 et seq. et seq. — Ed.
Lectures on Metaphysics, vol. ii. p. 368
112 LECTURES ON LOGIC.
LECT. volition involves tlie supposition of an absolute com-
^ mencement of volition, that is, of a volition which is
a cause, but is not itself, qua cause, an effect. 2°,
That the absolute commencement of volition, or of
aught else, cannot be conceived, that is, cannot be
directly or positively thought as possible. So far he is
correct ; but when he goes on to apply these princi-
ples by arguing, (and be it observed this syllogism
lies at the root of all the reasonings for necessity),
Whatevei' is inconceivable is im2')ossihle ; hut the sup-
2)osition of the absolute comme7iGeme7it of volition is
inconceivable ; the7'efore, the supposition of the abso-
lute coTYimencement of volition {the condition of free
will) is impossible, — we may here demur to the sump-
tion, and ask him, — Can he positively conceive the
opposite contradictory of the absolute commencement,
that is, an infinite series of relative non-commence-
ments 1 If he answers, as he must, that he cannot,
we may again ask him, — By what right he assumed
as a self-evident axiom for his sumption, the proposi-
tion, — that ivhatever is inconceivable is impossible, or
by what right he could subsume his minor premise,
when by his own confession he allows that the oppo-
site contradictory of his minor premise, that is, the
very proposition he is apagogically proving, is, like-
wise, inconceivable, and, therefore, on the principle of
his sumption, likewise impossible.
And in the Thc samc inconsequence would equally apply to
LfbcrtaHan I'bie Libertarian, who should, attempt to prove that
i^TehTiftf free-will must be allowed, on the ground, that its
ree-wiii. QQi-|^^j.r^(ji(}tory opposltc is impossible, because incon-
ceivable. He cannot prove his thesis by such a pro-
cess ; in fact, by all speculative reasoning from the
LECTUEES ON LOGIC. 113
conditions of thought, the two doctrines are {?i ceqidli- lect.
hrio; — both are equally possible, — both are equally in- -^ — '—
conceivable. It is only when the Libertarian descends
to arguments drawn from the fact of the Moral Law
and its conditions, that he is able to throw in reasons
which incline the balance in his favour.
On these matters I, however, at present only touch,
in order to show you under what head of Error these
reasonings would naturally fall.
Leaving, therefore, or adjourning, the consideration Weakness
of the imbecility of the human intellect in general, portioned
I shall now take into view, as a source of logical error, the several
the Weakness or Disproportioned Strength of the sev- Fatuities, -
eral Cognitive Faculties. Now, as the Cognitive Fa- knor.
culties in man consist partly of certain Lower Powers, paSeTof
which he possesses in common with other sensible ^g^'^owerami
existences, namely, the Presentative, the Eetentive, the '"^ ^^'s^"'''-
Eepresentative, and the Eeproductive Faculties, and
partly of certain Higher Powers, in virtue of which he
enters into the rank of intelligent existences, namely,
the Elaborative and Regulative Faculties, — it will be
proper to consider the powers of these two classes
severally in succession, in so far as they may afford the
causes or occasions of error.
Of the lower class, the first faculty in order is the i. The
Presentative or Acquisitive Faculty. This, as you ciass,—
remember, is divided into two, viz. into the faculty sentative
/» 1 Faculty.
which presents us with the phpenomena oi the outer
world, and into the faculty which presents us with the
phfenomena of the inner." The former is External
Perception, or External Sense ; the latter is Self-con-
sciousness, Internal Perception, or Internal Sense. I
a See Lectures on Metaphysics, vol. ii. p. 23 et seq. — Ed.
VOL. II. H
— as a
source of
Error.
lU LECTURES ON LOGIC.
LECT. commence, therefore, with the Faculty of External
'— Perception, in relation to which I give you the follow-
ing paragraph.
Par.xcvii. '^ XCVII. When aught is presented through the
PercepTionl outcr scuses, there are two conditions necessary
for its adequate perception : — 1°, The relative Or-
gans must be present, and in a condition to dis-
charge their functions ; and 2°, The Objects them-
selves must bear a certain relation to these or-
gans, so that the latter shall be suitably affected,
and thereby the former suitably apprehended.
It is possible, therefore, that, partly through the
altered condition of the organs, partly through
the altered situation of the objects, dissimilar
presentations of the same, and similar presenta-
tions of different, objects, may be the result."
Expiica- "In the first place, without the organs specially
Conditions subscrvieut to External Perception, — without the eye,
adequate ^^^^ ^^^' ^^v scusible perccptious of a precise and de-
Extefnai**^ terminate character, such, for example, as colour or
Perception. gQ^JJ(^^ ^yq j^q^ competcut to mau. In the second
place, to perform their functions, these organs must be
in a healthy or normal state ; for if this condition be
not fulfilled, the presentations which they furnish are
null, incomplete, or false. But, in the third place,
even if the organs of sense are sound and perfect, the
objects to be presented and perceived must stand to
these organs in a certain relation, — must bear to them
a certain proportion ; for, otherwise, the objects can-
not be presented at all, or cannot be perceived without
a Krug, Lof/iJc, gl 38.— Ed. [Cf. p. 273. Bachmann, Lo[/!l; § 407, p.
Caro, Nourelle Logiquc, part ii. ch. vi. 553.]
LECTURES ON LOGIC. 115
illusion. The sounds, for example, which we are to lect.
XXX.
hear, must neither be too high nor too low in quality ; — — ^
the bodies which we are to see, must neither be too inusLs of
near nor too distant, — must neither be too feebly nor
too intensely illuminated. In relation to the second
condition, there are given, in consequence of the al-
tered state of the organs, on the one hand, different
presentations of the same object ; — thus to a person
who has waxed purblind, his friend appears as an utter
stranger, the eye now presenting its objects with less
clearness and distinctness. On the other hand, there
are given the same, or undistinguishably similar, presen-
tations of different objects ; — thus to a person in the
jaundice, all things are presented yellow. In relation
to the third condition, from the altered position of
objects, there are, in like manner, determined, on the
one hand, different presentations of the same objects,
— as when the stick which appears straight in the air
appears crooked when partially immersed in water; and,
on the other hand, identical presentations of different
objects, as when a man and a horse appear in the dis-
tance to be so similar, that the one cannot be discrim-
inated from the other. In all these cases, these illu-
sions are determined, — illusions which may easily be-
come the occasions of false judgments.""
" In regard to the detection of such illusions and Precautions
obviating the error to which they lead, it behoves us to the detec-
,._-,-. . -j^-^ . - tion of illu-
to take the lollowmg precautions. We must, m thesionsof the
first place, examine the state of the organ. If found obviatmg
1j16 errors
defective, we must endeavour to restore it to perfec- to wiiich
tion, but if this cannot be done, we must ascertain
the extent and nature of the evil, in order to be upon
o Krug, Lofjil-, § 138. Anm. — Ed.
IIG
LECTURES ON LOGIC.
LECT.
XXX.
our guard in regard to quality and degree of tlie false
presentation.
" In tlie second place, we must examine the relative
situation of the object, and if this be not accommo-
dated to the organ, we must either obviate the dis-
proportion and remove the media which occasion the
illusion, or repeat the observation under different cir-
cumstances, compare these, and thus obtain the means
of making an ideal abstraction of the disturbing
causes." «
In regard to the other Presentative Faculty, — the
Faculty of Self-consciousness, — Internal Perception,
or Internal Sense, as we know less of the material
conditions which modify its action, we are unable to
ascertain so precisely the nature of the illusions of
which it may be the source. In reference to this sub-
ject you may take the following paragraph.
Par. XCVIIL
b. Self- con-
sciousness,
— as a
source of
Error.
^ XCVIIL The faculty of Self-consciousness, or
Internal Sense, is subject to various changes,
which either modify our apprehensions of ob-
jects, or influence the manner in which we judge
concerning them. In so far, therefore, as false
judgments are thus occasioned. Self-consciousness
is a source of error,^
Explica-
tion.
Self- con-
sciousness
varies in
intensity.
It is a matter of ordinary observation, that the
vivacity with which we are conscious of the various
phaenomena of mind, difi'ers not only at different times,
in different states of health, and in different degrees
of mental freshness and exhaustion, but, at the same
a Krug, LofjUc, § 155. — Ed.
B Krug, LoyU,; § I.IO.— Ed.
LECTURES ON LOGIC. 117
time, differs in regard to tlie different kinds of tliese lect.
. XXX
phsenomena themselves. According to the greater or 1^-
less intensity of this faculty, the same thoughts of
which we are conscious are, at one time, clear and
distinct, at another, obscure and confused. At one
time we are almost wholly incapable of reflection, and
every act of self-attention is forced and irksome, and
differences the most marked pass unnoticed ; while,
at another, our self-consciousness is alert, all its appli-
cations jileasiug, and the most faint and fugitive
j)h8enomena arrested and observed. On one occasion,
self-consciousness, as a reflective cognition, is strong ;
on another, all reflection is extinguished in the inten-
sity of the direct consciousness of feeling or desire. In
one state of mind our representations are feeble; in
another, they are so lively that they are mistaken for
external realities. Our self-consciousness may thus
be the occasion of frequent error : for, according to its
various modifications, we may form the most 0|)posite
judgments concerning the same things, — pronouncing
them, for example, now to be agreeable, now to be
disagreeable, according as our Internal Sense is vari-
ously affected.
The next is the Eetentive or Conservative Faculty,
— Memory strictly so called ; in reference to which I
give you the following paragraph.
IF XCIX. Memory, or the Conservative Faculty, Par. xcix.
is the occasion of Error, both when too weak and -^as a
when too strong. When too weak, the complement Error.
of cognitions w^hich it retains is small and indis-
tinct, and the Understanding or Elaborative
Faculty is, consequently, unable adequately to
118 LECTURES ON LOGIC.
LECT. j^iclg® concerning the similarity and differences
11- of its representations and concepts. When too
strong, the Understanding is overwhelmed with
the multitude of acquired cognitions simultane-
ously forced upon it, so that it is unable calmly
and deliberately to compare and discriminate
these, a
Expii.a- That both these extremes, — that both the insuffi-
cient and the superfluous vigour of the Conservative
Faculty are severally the sources of error, it will not
require many observations to make apparent.
FecUc lu regard to a feeble memory, it is manifest that a
multitude of false judgments must inevitably arise
from an incapacity in this faculty to preserve the
observations committed to its keeping. In conse-
quence of this incapacity, if a cognition be not wholly
lost, it is lost at least in part, and the circumstances
of time, place, persons and things confounded with
each other. For example, — I may recollect the tenor
of a passage I have read, but from defect of memory
may attribute to one author what really belongs to
another. Thus a botanist may judge two difierent
plants to be identical in species, having forgotten the
differential characters by which they w^ere discrimin-
ated ; or he may hold the same plant to be two different
species, having examined it at different times and
places.^
Strong Though nothiug could be more erroneous than a
general and unqualified decision, that a great memory
is incompatible with a sound judgment, yet it is an
observation confirmed by the experience of all ages
a [Of. Bachmnnn, Loyik, § iOS.] j8 Krug, Lo^jll; § 141. Anra.— Ed.
XXX.
LECTUEES ON LOGIC. 110
and countries, not only that a great memory is no lect
condition of high intellectual talent, but that great
memories are very frequently found in combination
with comparatively feeble powers of thought." The
truth seems to be, that where a vigorous memory is
conjoined with a vigorous intellect, not only does the
force of the subsidiary faculty not detract from the
strength of the principal, but, on the contrary, tends
to confer on it a still higher power ; whereas when
the inferior faculty is disproportionately strong, that
so far from nourishing and corroborating the superior,
it tends to reduce this faculty to a lower level than
that at which it would have stood, if united with a
less overj^owering subsidiary. The greater the maga-
zine of various knowledge which the memory contains,
the better for the understanding, provided the un-
derstanding can reduce this various knowledge to
order and subjection " A great memory is the prin-
cipal condition of bringing before the mind many
different representations and notions at once, or in
rapid succession. This simultaneous or nearly simul-
taneous presence disturbs, however, the tranquil com-
parison of a small number of ideas, which, if it shall
judge aright, the intellect must contemplate with a
fixed and steady attention." ^ Now, where an intellect
possesses the power of concentration in a high degree,
it will not be harassed in its meditations by the ojBS.-
cious intrusions of the subordinate faculties, however
vigorous these in themselves may be, but will control
their vigour by exhausting in its own operations the
o Compare Lectures on Metaphysics, Muets, quoted by Stewart, Elem., Part
vol. ii. p. 223. — Ed. iii. ch. i. sect. vi. Collected Works,
/3 Diderot, Lettre sur Ics Suurcls et vol. iv. p. 249.
120 LECTUEES ON LOGIC.
LECT. whole applicable energy of mind. AVliereas where
'— the inferior is more vigorous than the superior, it will,
in like manner, engross in its own function the dis-
posable amount of activity, and overwhelm the prin-
cipal faculty with materials, many even in proportion
as it is able to elaborate few. This appears to me the
reason, why men of strong memories are so often men
of proportionally weak judgments, and why so many
errors arise from the possession of a faculty, the per-
fection of which ought to exempt them from many
mistaken judgments.
Remotiics As to thc remedy for these opposite extremes. The
opposite former, — the imbecility of Memory, — can only be allevi-
ated by invigorating the capacity of Retention through
mnemonic exercises and methods ; the latter, — the in-
ordinate vigour of Memory, — by cultivating the Under-
standing to the neglect of the Conservative Faculty.
It will, likewise, be necessary to be upon our guard
aofainst the errors orio-inatino; in these counter sources.
In the one case distrusting the accuracy of the facts,
in the other, the accuracy of their elaboration. *
3. The Re- The ncxt faculty is the Reproductive. This, when
Faculty, its Operation is voluntarily exerted, is called Recollec-
tion or Reminiscence ; when it energises spontane-
ously or without volition, it is called Suggestion. The
laws by which it is governed in either case, but espe-
cially in the latter, are called the Laws of Mental
Association. This Reproductive Faculty, like the
Retentive, is the cause of error, both if its vigour be
defective, or if it be too strong. I shall consider Re-
collection and Suggestion severally and apart. In
regard to the former I give you the following para-
graph.
a Cf. Ki'ug_, Lvijllc, § 156. Anm. — Ed.
LECTURES ON LOGIC. 121
IT C. The Eeproductive Faculty, in so far lect,
XXX.
Par. C.
as it is voluntarily exercised, as Eeminiscence,
becomes a source of Error as it is either too p . .
a. Keiniuis-
sluggish or too prompt, precisely as the Reten- ^^^Ijll^^of
tive Faculty, combined with which it constitutes ^'■™''-
Memory in the looser signification.
It is necessary to say very little in special reference Ex-piica-
to Reminiscence, for what was said in regard to the Reminis-
Conservative Faculty or Memory Proper in its higher its undue
vigour, was applicable to, and in fact supposed a cor- '
responding degree of, the Reproductive. For, however
great may be the mass of cognitions retained in the
mind, that is, out of consciousness but potentially
capable of being called into consciousness, these can
never of themselves oppress the Understanding by
their simultaneous crowding or rapid succession, if
the faculty by which they are revoked into conscious-
ness be inert ; whereas, if this revocative faculty be
comparatively alert and vigorous, a smaller magazine
of retained cognitions may suffice to harass the intel-
lect with a ceaseless supply of materials too profuse
for its capacity of elaboration.
On the other hand, the inactivity of our Eecollec- its inani-
tion is a source of error, precisely as the weakness of ^' ^'
our Memory proper ; for it is of the same effect in
relation to our judgments, whether the cognitions re-
quisite for a decision be not retained in the mind, or
whether, being retained, they are not recalled into
consciousness by Reminiscence.
In regard to Suggestion, or the Reproductive Faculty
operating spontaneously, that is, not in subservience
to an act of "Will, — I shall give you the following
paragraph.
tion.
122 LECTURES ON LOGIC.
LECT. IF CI. As our Coo-nitions, Feelings, and Desires
XXX
L are connected together by what are called the
Par CI. Laws of Associatioii, and as each link in the
b. ougges- •'
tion,- as a chain of thought suo-o-ests or awakens into con-
source of ^ ^^
Error. sciousness some other in conformity to these
Laws, — these Laws, as they bestow a strong sub-
jective connection on thoughts and objects of a
wholly arbitrary union, frequently occasion great
confusion and error in our j adgments.
Expiica- " Even in methodical thinking, we do not connect
all our thoughts intentionally and rationally, but
many press forward into the train, either in conse-
quence of some external impression, or in virtue of
certain internal relations, which, however, are not of a
logical dependency. Thus, thoughts tend to suggest
each other, which have reference to things of which
we were previously cognisant as coexistent, or as im-
mediately consequent, which have been apprehended
as bearing a resemblance to each other, or which have
stood together in reciprocal and striking contrast.
This connection, though precarious and non-logical, is
thus, however, governed by certain laws, which have
been called the Laivs of Association" " These laws,
which I have just enumerated, viz. the Law of Co-
existence or Simultaneity, the Law of Continuity or
Immediate Succession, the Law of Similarity, and the
Law of Contrast, are all only special modifications of
one general law which I would call the Law of Redin-
tegration ^ ; that is, the principle according to which
whatever has previously formed a part of one total
act of consciousness, tends, when itself recalled into
a Krug, Zo^//i-, § 144. Anm.— Ed. ii. p. 233 ei: scj. — Eo.
^ See Lectures on ^Ictajph/jtsics, vol.
LECTURES OX LOGIC. 123
consciousness, to reproduce along with it the other lect.
parts of that original whole. But though these tend- ^ ' ' "
encies be denominated laivs, the influence which they
exert, though often strong and sometimes irresistible,
is only contingent ; for it frequently happens that
thoughts which have previously stood to each other in
one or other of the four relations do not suo-o-est each
other. The Laws of Association stand, therefore, on
a very different footing from the laws of logical con-
nection. But those Laws of Association, contingent
though they be, exert a great and often a very perni-
cious influence upon thought, inasmuch as by the in-
voluntary intrusion of representations into the mental
chain, which are wholly irrelevant to the matter in
hand, there arises a perplexed and redundant tissue
of thouglit, into which false characters may easily
find admission, and in which true characters may
easily be overlooked.'' But this is not all. For, by
being once blended together in our consciousness,
things really distinct in their nature tend again natu-
rally to reassociate, and, at every repetition of this
conjunction, this tendency is fortified, and their mu-
tual suggestion rendered more certain and irresistible.
It is in virtue of this principle of Association and influence
Custom, that things are clothed by us with the preca- ation in
rious attributes of deformity or beauty ; and some Taste,
philosophers have gone so far as to maintain that our
principles of Taste are exclusively dependent on the
accidents of Association. But if this be an exagger-
ation, it is impossible to deny that Association en-
joys an extensive jurisdiction in the empire of taste,
and, in particular, that fashion is almost wholly sub-
ject to its control.
o Kriig, Lofjil, § 14-1. Aum.— Ed.
124 LECTURES ON LOGIC.
LECT. On tliis subject I may quote a few sentences from
XXX
- the first volume of Mr Stewart's Elements. " In mat-
quoted' ters of Taste, the effects which we consider, are pro-
duced on the mind itself, and are accompanied either
with pleasure or with pain. Hence the tendency to
casual association is much stronger than it commonly
is with respect to physical events ; and when such
associations are once formed, as they do not lead to
any important inconvenience, similar to those which
result from physical mistakes, they are not so likely
to be corrected by mere experience, unassisted l)y
study. To this it is owing that the influence of asso-
ciation on our judgments concerning beauty and de-
formity, is still more remarkable than on our specula-
tive conclusions ; a circumstance wdiich has led some
philosophers to suppose that association is sufficient
to account for the origin of these notions, and that
there is no such thing as a standard of taste, founded
on the principles of the human constitution. But this
is undoubtedly pushing the theory a great deal too
far. The association of ideas can never account for
the origin of a new notion, or of a joleasure essentially
different from all the others which we know. It may,
indeed, enable us to conceive how a thing indifferent
in itself may become a source of pleasure, by being
connected in the mind with something else which is
naturally agreeable ; but it presupposes, in every in-
stance, the existence of those notions and those feel-
ings which it is its province to combine : insomuch
that, I apprehend, it will be found, wherever associa-
tion produces a change in our judgments on matters
of taste, it does so by co-operating with some natural
principle of the mind, and implies the existence of
certain original sources of pleasure and uneasiness.
LECTUKES ON LOGIC. 125
" A mode of dress, wliicli at first appeared awk- lect,
ward, acquires, in a few weeks or months, the appear-
ance of elegance. By being accustomed to see it
worn by those whom we consider as models of taste,
it becomes associated with the agreeable impressions
which we receive from the ease and grace and refine-
ment of their manners. When it pleases by itself, the
efiect is to be ascribed, not to the object actually be-
fore us, but to the impressions with w^hich it has been
generally connected, and which it naturally recalls to
the mind.
" This observation points out the cause of the per-
petual vicissitudes in dress, and in everything whose
chief recommendation arises from fashion. It is evi-
dent that, as far as the agreeable effect of an ornament
arises from association, the effect will continue only
while it is confined to the higher orders. When it is
adopted by the multitude, it not only ceases to be
associated with ideas of taste and refinement, but it is
associated with ideas of affectation, absurd imitation,
and vulgarity. It is accordingly laid aside by the
higher orders, who studiously avoid every cii^cum-
stance in external appearance which is debased by low
and common use ; and they are led to exercise their
invention in the introduction of some new peculiari-
ties, which first become fashionable, then common, and
last of all, are abandoned as vulgar." "*
" Our moral judgments, too, may be modified, and
even perverted to a certain degree, in consequence of
the operation of the same principle. In the same
manner in which a person who is regarded as a model
of taste may introduce, by his example, an absurd or
fantastical dress ; so a man of splendid virtues may
a Elements, vol. i., Part i. chap. v. Collected Worl-s, ii. p. 3"22 et scq.
126 LECTURES ON LOGIC.
LECT. attract some esteem also to his imperfections ; and, if
'— placed in a conspicuous situation, may render his vices
and follies objects of general imitation among the
multitude.
" ' In the reign of Charles II.,' says Mr Smith," ' a
degree of licentiousness was deemed the characteris-
tic of a liberal education. It was connected, according
to the notions of those times, with generosity, sincer-
ity, magnanimity, loyalty ; and proved that the per-
son who acted in this manner was a gentleman, and
not a puritan. Severity of manners and regularity
of conduct, on the other hand, were altogether un-
fashionable, and were connected, in the imagination of
that age, with cant, cunning, hypocrisy, and low man-
ners. To superficial minds the vices of the great seem
at all times agreeable. They connect them not only
with the splendour of fortune, but with many superior
virtues which they ascribe to their superiors ; with the
spirit of freedom and independency ; with frankness,
generosity, humanity, and politeness. The virtues of
the inferior ranks of people, on the contrary, — their
parsimonious frugality, their painful industry, and
rigid adherence to rules, seem to them mean and dis-
agreeable. They connect them both with the mean-
ness of the station to which these qualities commonly
belong, and with many great vices which they suppose
usually accompany them ; such as an abject, cowardly,
ill-natured, lying, pilfering disposition.' "^
Condiiiac " In general," says Condillac, " the impression we
the influ^ experience in the different circumstances of life, makes
Ab^sodation. US assoclatc ideas with a force which renders them
ever after for us indissoluble. We cannot, for ex-
o Thcorii of Moral Sentivients, P Elements, vol. i. c. v. § 3. Col-
Piirt V. c. 2. — Ed. lecfed Works, vol. ii. p. 335.
LECTURES ON LOGIC. 127
ample, frequent tlie society of our fellow-men without lect.
insensibly associating the notions of certain intellec- ' ' ^ '
tual or moral qualities with certain corporeal charac-
ters. This is the reason why persons of a decided
physiognomy please or displease us more than others ;
for a physiognomy is only an assemblage of characters,
with which we have associated notions which are not
suggested without an accompaniment of satisfaction
or disgust. It is not, therefore, to be marvelled at that
we judge men according to their physiognomy, and
that we sometimes feel towards them at first sight
aversion or inclination. In consequence of these
associations, we are often vehemently prepossessed in
favour of certain individuals, and no less violently
disposed against others. It is because all that strikes
us in our friends or in our enemies is associated with
the ao-reeable or the disa2;reeable feelino; which we
severally experience ; and because the faults of the
former borrow always something pleasing from their
amiable qualities ; whereas the amiable qualities of
the latter seem always to participate of their vices.
Hence it is that these associations exert a powerful
influence on our whole conduct. They foster our love
or hatred ; enhance our esteem or contempt ; excite
our gratitude or indignation ; and produce those sym-
pathies, — those antipathies, or those capricious inclin-
ations, for which we are sometimes sorely puzzled to
render a reason. Descartes tells us that through life
he had always felt a strong predilection for squint
eyes, — which he explains by the circumstance, that
the nursery-maid by whom he had been kindly tended,
and to whom as a child he was, consequently, much
attached, had this defect." '^ 'S Gravesande, I think it
o Oviijlne d:s Connohsances Ilumalnes, sect. ii. ch. ix. § SO. — Ed.
128 LECTURES ON LOGIC.
LECT. is, who tells us lie knew a man, and a man otherwise
^ L of sense, who had a severe fall from a waggon ; and
thereafter he could never enter a waggon without fear
and trembling, though he daily used, without appre-
hension, another and far more dangerous vehicle." A
girl once and again sees her mother or maid fainting
and vociferating at the appearance of a mouse ; if she
has afterwards to escajDC from danger, she will rather
pass through flames than take a patent way, if ob-
structed by a ridiculiis miis. A remarkable example
of the false judgments arising from this principle of
association, is recorded by Herodotus and Justin, in
reference to the war of the Scythians with their slaves.
The slaves, after they had repeatedly repulsed several
attacks with arms, were incontinently put to flight
when their masters came out against them with their
whips.'^
I shall now ofi'er an observation in regard to the
appropriate remedy for this evil influence of Associa-
tion.
Only re- The ouly uicau by which we can become aware of,
"he influence couutcract, aud overcome, this besetting v/eakness of
tioni^rtile our nature, is Philosophy, — the PhilosojDhy of the
of"he^"'"^ Human Mind ; and this studied both in the conscious-
MhiX" ness of the individual, and in the history of the spe-
cies. The philosophy of mind, as studied in the con-
sciousness of the individual, exhibits to us the source
and nature of the illusion. It accustoms us to discri-
minate the casual, from the necessary, combinations
of thought ; it sharpens and corroborates our facul-
a Tntroductio ad Philosopliiam, Lo- low are also from 'S Gravesaiide. —
yica, c. 26. The example, however, is Ed.
given as a supposed case, not as a ^ Herod., iv. 3. Justin., ii. 5
fact. The two instances which fol- Ed.
LECTURES ON LOGIC. 129
ties, encourages our reason to revolt asfainst the blind lect.
. . . XXX.
preformations of opinion, and finally enables us to '-
break through the enchanted circle mthin which Cus-
tom and Association had enclosed us. But in the
accomplishment of this end, we are greatly aided by
the study of man under the various circumstances
which have concurred in modifying his intellectual
and moral character. In the great spectacle of his-
tory, we behold in different ages and countries the
predominance of different systems of association, and
these ages and countries are, consequently, distin-
guished by the prevalence of different systems of
opinions. But all is not fluctuating ; and, amid the
ceaseless changes of accidental circumstances and pre-
carious beliefs, we behold some principles ever active,
and some truths always commanding a recognition.
We thus obtain the means of discriminating, in so
far as our unassisted reason is conversant about mere
worldly concerns, between what is of universal and
necessary certainty, and what is only of local and
temporary acceptation ; and, in reference to the latter,
in witnessing the influence of an arbitrary association
in imposing the most irrational opinions on our fel-
low men, our eyes are opened, and we are warned of
the danger from the same illusion to ourselves. And
as the philosophy of man affords us at once the indi-
cation and the remedy of this illusion, so the philo-
sophy of man does this exclusively and alone. Our
irrational associations, our habits of groundless credu-
lity and of arbitrary scepticism, find no medicine in
the study of aught beyond the domain of mind itself.
As Goethe has well observed, " Mathematics remove
no prejudice ; they cannot mitigate obstinacy, or
i VOL. II. I
130 LECTUEES ON LOGIC.
LECT. temper party-spirit ;"« in a word, as to any moral
XXX.
influence upon the mind they are absolutely null.
Hence we may well explain the aversion of Socrates
for these studies, if carried beyond a very limited
extent.
The Repre- The ncxt faculty in order is the Eepresentative, or
sentative -^ . . ..- ..,
Faculty, Imamnatiou proper, which consists in the OTeater or less
or Imagiua- pit • t • •iti
tion Proper, power of lioldiug up an ideal object in the light of
consciousness. The energy of Representation, though
dependent on Retention and Reproduction, is not to
be identified with these operations. For though these
three functions (I mean Retention, Reproduction, and
Representation), immediately suppose, and are immedi-
ately dependent on, each other, they are still mani-
festly discriminated as different qualities of mind, in-
asmuch as they stand to each other in no determinate
proportion. We find, for example, in some indivi-
duals the capacity of Retention strong, but the Re-
productive and Representative Faculties sluggish and
weak. In others, again, the Conservative tenacity is
feeble, but the Reproductive and Representative ener-
gies prompt and vivid ; while in others the power of
Reproduction may be vigorous, but what is recalled is
never pictured in a clear and distinct consciousness.
It will be generally, indeed, admitted, that a strong re-
tentive memory does not infer a prompt recollection ;
and still more, that a strong memory and a prompt
recollection do not infer a vivid imagination. These,
therefore, though variously confounded by philoso-
phers, we are warranted, I think, in viewing as elemen-
tary qualities of mind, which ought to be theoretically
distinguished. Limiting, therefore, the term Imagina-
a Wei-Jce, xxii. p. 258. Quoted by Scheidler, Psycliolorjic, p. 146.
LECTURES ON LOGIC. 131
tion to the mere Faculty of Representing in a more or lect.
less vivacious manner an ideal object, — this Faculty ' ' ^ '
is the source of errors which I shall comprise in the
following paragraph.
% CII. Imagination, or the Faculty of Repre- Par. cii.
. -, -, . . ,, , , 4. Imagina-
sentmg with more or less vivacity a recalled ob- tion, —as a
„ ... 1 p -n 11 source of
ject 01 cognition, is the source ot Horrors, both Error.
when it is too languid and when it is too vio;or-
ous. In the former case, the object is represent-
ed obscurely and indistinctly ; in the latter, the
ideal representation affords the illusive appear-
ance of a sensible presentation.
A strong imagination, that is, the power of holding Expiica-
up any ideal object to the mind in clear and steady Necessity
colours, is a faculty necessary to the poet and to the tion in"
artist ; but not to them alone. It is almost equally pursuits.
requisite for the successful cultivation of every scien-
tific pursuit ; and, though differently applied, and
different in the character of its representations, it
may well be doubted whether Aristotle did not pos-
sess as powerful an imagination as Homer. The
vigour and perfection of this faculty is seen, not so
much in the representation of individual objects and
fragmentary sciences, as in the representation of sys-
tems. In the better ages of antiquity the perfection, Diverse
— the beauty, of all works of taste, whether in Poetry, Lticsof Art
Eloquence, Sculpture, Painting, or Music, was princi- Lnd modem
pally estimated from the symmetry or proportion of ""''''■
all the parts to each other, and to the whole which
they together constituted ; and it was only in subser-
vience to this general harmony that the beauty of the
several parts was appreciated. In the criticism of
132 LECTURES ON LOGIC.
LECT. modern times, on the contrary, tlie reverse is true ;
'— and we are disposed to look more to the obtrusive qua-
lities of details than to the keeping and unison of a
whole. Our works of art are, in general, like kinds
of assorted patch-work ; — not systems of parts all
subdued in conformity to one ideal totality, but co-
ordinations of independent fragments, among which
a "pz^7'pwci^5 2^cmni(s" seldom comes amiss. The rea-
son of this difference in taste seems to be, what at first
sight may seem the reverse, that in antiquity not the
Reason but the Imagination was the more vigorous ; —
that the Imagination was able to represent simultane-
ously a more comprehensive system ; and thus the
several parts being regarded and valued only as con-
ducive to the general result, — these parts never ob-
tained that individual importance, which would have
fallen to them had they been only created, and only
considered, for themselves. Now this power of repre-
senting to the mind a complex system in all its bear-
ings, is not less requisite to the philosopher than to
the poet, though the representation be different in
kind ; and the nature of the philosophic representa-
tions, as not concrete and palpable like the poetical,
supposes a more arduous operation, and, therefore,
even a more vigorous faculty. But Imagination, in
the one case and in the other, requires in proportion
to its own power a powerful intellect ; for imagina-
tion is not poetry nor philosophy, but only the condi-
tion of the one and of the other.
Errors But to speak now of the Errors which arise from
from the"" the disproportion between the Imagination and the
dispropor- j^(;jgj3^gjjl^ . — ii^Qj originate either in the weakness, or
gTuatiou"and in tho iuordinatc strength, of the former.
Judgment. j^^ regard to the errors which arise from the imbe-
LECTURES ON LOGIC. 133
cility of tlie Representative Faculty, it is not difficult lect.
to conceive how this imbecility may become a cause ^^ ^'
of erroneous judgment. The Elaborative Faculty, in jn'^f^^^'the
order to judge, requires an object, — requires certain o7ima^lna-
differences to be given. Now, if the imagination be *''''^-
weak and languid, the objects represented by it will
be given in such confusion and obscurity, that their
differences are either null or evanescent, and judgment
thus rendered either impossible, or possible only with
the probability of error. In these circumstances, to
secure itself from failure, the intellect must not at-
tempt to rise above the actual presentations of sense ;
it must not attempt any ideal analysis or synthesis, —
it must abandon all free and self-active elaboration,
and all hope of a successful cultivation of knowledge.
Again, in regard to the opposite errors, those arising prom its
from the disproportioned vivacity of imagination, — t'oS*""
these are equally apparent. In this case the renewed '"''^^'y-
or newly-modified representations make an equal im-
pression on the mind as the original presentations,
and are, consequently, liable to be mistaken for these.
Even during the perception of real objects, a too lively
imagination mingles itself with the observation, which
it thus corrupts and falsifies. Thus arises what is
logically called the vitimn suhreptionis."' This is fre-
quently seen in those pretended observations made by
theorists in support of their hypotheses, in which, if
even the possibility be left for imagination to inter-
fere, imagination is sure to fiU up all that the senses
may leave vacant. In this case the observers are at
once dupes and deceivers, in the words of Tacitus
" Fingunt simul creduntque." ^
a Krug, Lorjik, § 142. Anm.— Ed. on Metaphysics, vol. i. p. 76.— Ed.
/8 Hist. lib. ii, c. 8. See Lectures
134
LECTURES ON LOGIC.
LECT.
XXX.
Remedies
for these
defects of
the Imagin-
ation.
In reirard to tlie remedies for these defects of tlie
Eepresentative Faculty ; — in the former case, the only
alleviation that can be proposed for a feeble Imagina-
tion, is to animate it by the contemplation and study
of those works of art which are the products of a strong
Phantasy, and which tend to awaken in the student a
corresponding energy of that faculty. On the other
hand, a too powerful imagination is to be quelled and
regulated by abstract thinking, and the study of phi-
losophical, perhaps of mathematical, science."
The faculty which next follows, is the Elaborative
Faculty, Comparison, or the Faculty of Relations.
This is the Understanding, in its three functions of
Conception, Judgment, and Eeasoning. On this fa-
culty take the following paragraph.
Par. cm.
5. Elabor-
ative Fa-
culty, — as
a source of
Error,
H cm. The Affections and the Lower Cog-
nitive Faculties afford the sources and occasions
of error ; but it is the Elaborative Faculty, Un-
derstanding, Comparison, or Judgment, which
truly errs. This faculty does not, however, err
from strength or over-activity, but from inac-
tion ; and this inaction arises either from natural
weakness, from want of exercise, or from the im-
potence of attention. ^
Explica-
tion.
Error does
not lie in
tlie condi-
tions of our
Higher
Faculties,
but is pos-
I formerly observed that error does not lie in the
conditions of our higher faculties themselves, and that
these faculties are not, by their own laws, determined
to false judgments or conclusions : —
" Nam ueque decipitur ratio, uec deciiDit unquam." y
a Cf. Krug, Lor/ik, § 156. Anm. — Fries, Loyifc, § 108. Bachmanu, Zo*///;,
Ed. §411.]
/3 Krug, Lofj'ik, § 148. — Ed. [Cf. y See above, vol. ii. p. 77.— Ed.
LECTURES ON LOGIC. 135
If this were otherwdse, all knowledge would be impos- lect.
sible, — tlie root of our nature would be a lie. "But
in the application of the laws of our higher faculties application
to determinate cases, many errors are possible ; and l\ thosl"^^^^
these errors may actually be occasioned by a variety ietelmTnate
of circumstances. Thus, it is a law of our intelligence, '"'^''^*
that no event, no phenomenon, can be thought as
absolutely beginning to be ; we cannot but think that
all its constituent elements had a virtual existence
prior to their concurrence, to necessitate its manifest-
ation to us ; we are thus unable to accord to it more
than a relative commencement, in other words, we
are constrained to look upon it as the effect of ante-
cedent causes. Now though the law itself of our in-
telligence, — that a cause there is for every event, — be
altogether exempt from error, yet in the application
of this law to individual cases, that is, in the attribu-
tion of determinate causes to determinate effects, we
are easily liable to go wrong. For we do not know,
except from experience and induction, what particular
antecedents are the causes of particular consequents ;
and if our knowledge of this relation be imperfectly
generalised, or if we extend it by a false analogy to
cases not included within our observation, error is
the inevitable consequence. But in all this there is
no fault, no failure, of intelligence, there is only a de-
ficiency, — a deficiency in the activity of intelligence,
while the Will determines us to a decision before the
Understanding has become fully conscious of certainty.
The defective action of the Understanding may arise Defective
from three causes. In the first place, the faculty of the Under-
Judgment may by nature be too feeble. This is the may arise
case in idiots and weak persons. In the second place, causes.
though not by nature incompetent to judge, the in- feebleness.
136
LECTURES ON LOGIC.
LECT. tellect may bo without the necessary experience, —
L may not possess the grounds on which a correct judg-
nocelsTry"^ mcut must bc fouudcd. In the third place, and this
experience, 'g ^^^ most frcquent cause of error, the failure of the
c. Incom- -■■
petency of uuderstandino; is from the incompetency of that act of
attention. _ _ ^ , ■■■ '' ^ ^
will which is called Atte^itioii. Attention is the vol-
untary direction of the mind upon an object, with the
intention of fully apprehending it. The cognitive
energy is thus, as it were, concentrated upon a single
point. We, therefore, say that the mind collects itself,
when it begins to be attentive ; on the contrary, that
it is distracted, when its attention is not turned upon
an object as it ought to be. This fixing — this con-
centration, of the mind upon an object can only be
carried to a certain degree, and continued for a certain
time. This degree and this continuance are both de-
pendent upon bodily circumstances ; and they are
also frequently interrupted or suspended by the intru-
sion of certain collateral objects, which are forced upon
the mind, either from without, by a strong and sudden
impression upon the senses, or from within, through
the influence of Association ; and these, when once
obtruded, gradually or at once divert the attention
from the original and principal object. If we are not
sufficiently attentive, or if the eflbrt which accompanies
the concentration of the mind upon a single object be
irksome, there arises hurry and thoughtlessness in
judging, inasmuch as we judge either before we have
fully sought out the grounds on which our decision
ought to proceed, or have competently examined their
validity and effect. It is hence manifest that a multi-
tude of errors is the inevitable consequence." «
a Krug, Lofjik, § 148. Aurn. lu aomo places slightly changed. — Ed.
LECTURES ON LOGIC. 137
In regard to the Eegulative Faculty, — Common lect.
Sense, — Intelligence, — vovs, — this is not in itself a ^ ^ ^ '
source of error. Errors may, however, arise either from JiVe^Fl!^'''
overlooking the laws or necessary principles which it "f^^]
not
properly a
source
Error.
of
does contain ; or by attributing to it, as necessary
and original data, what are only contingent general-
isations from experience, and, consequently, make no
part of its complement of native truths. But these
errors, it is evident, are not to be attributed to the Ee-
gulating Faculty itself, which is only a place or source
of principles, but to the imperfect operations of the
Understanding and Self-consciousness, in not pro-
perly observing and sifting the phsenomena which it
reveals.
Besides these sources of Error, which immediately Remote
originate in the several powers and faculties of mind, Erroi^in'the
there are others of a remoter origin arising from the habits de-
different habits which are determined by the differ- sex"'age, ^
ences of sex,« of age,^ of bodily constitution,'^ of stuutlonr'
-I , • /» inn, n c • /»• education,
education, oi rank, oi lortune, oi profession, of m- ice
tellectual pursuit. Of these, however, it is impossible
at present to attempt an analysis ; and I shall only
endeavour to afford you a few specimens, and to refer
you for information in regard to the others to the best
sources.
Intellectual pursuits or favourite studies, inasmuch s^eiecte.i
as these determine the mind to a one-sided cultiva- of Tcse'"
tion, that is, to the neglect of some, and to the dis- cultivation
proportioned development of other, of its faculties, are teiiectuai
among the most remarkable causes of error. This ^'°''®^^'
a [See Stewart, Elements, vol. iii. Crousaz, Logiquc, t. i. part i. sect. i.
part iii. sect. v. chap. i. Worls, vol. ch. v. § 15, p. 104.]
iv. p. 238 et seq.] y [See Crousaz, Lorjique, t. i. p. i.
/3 [Aristotle, Bliet., L. ii. c. 12. sect. i. ch. v. p. 91 et seq.l
138
LECTURES ON LOGIC.
LECT.
XXX.
This ex-
emplified
in three
different
phases.
Exclusive
cultivation.
1. Of the
powers of
Observa-
tion.
2. Of Meta-
physics.
3. Of Man
thematics.
Stewart
referred to.
partial or one-sided cultivation is exemplified in three
different phases. The first of these is shown in the
exclusive cultivation of the powers of Observation, to
the neglect of the higher faculties of the Understand-
ing. Of this type are your men of physical science.
In this department of knowledge there is chiefly de-
manded a patient habit of attention to details, in
order to detect phtenomena, and, these discovered,
their generalisation is usually so easy that there is
little exercise afibrded to the higher energies of Judg-
ment and Reasonino;. It was Bacon's boast that In-
duction, as applied to nature, would equalise all tal-
ents, level the aristocracy of genius, accomplish mar-
vels by co-operation and method, and leave little to
be done by the force of individual intellects. This
boast has been fulfilled ; Science has, by the Induc-
tive Process, been brought down to minds, who pre-
viously would have been incompetent for its cultiva-
tion, and physical knowledge now usefully occupies
many who would otherwise have been without any
rational pursuit. But the exclusive devotion to such
studies, if not combined with higher and graver specu-
lations, tends to wean the student from the more
vigorous efibrts of mind, which, though unamusing
and even irksome at the commencement, tend, how-
ever, to invigorate his nobler powers, and to prepare
him for the final fruition of the highest happiness of
his intellectual nature.
A partial cultivation of the intellect, opposite to
this, is given in the exclusive cultivation of Meta-
physics and of Mathematics. On this subject I may
refer you to some observations of Mr Stewart, in two
chapters entitled The Metaphysician and The Mathe-
LECTURES ON LOGIC. 139
matician, in the third volume of his Elements of the lect.
Philosophy of the Human Mind, — chapters clistin- -^^^'
guished equally by their candour and their depth of
observation. On this subject Mr Stewart's authority
is of the highest, inasmuch as he was distinguished in
both the departments of knowledge, the tendency of
which he so well develops.
140
LECTURES ON LOGIC.
LECTURE XXXI.
MODIFIED STOICHEIOLOGY.
SECTION II. — ERROR, — ITS CAUSES AND REMEDIES.
C. LANGUAGE — D. OBJECTS OF KNOWLEDGE.
LECT.
XXXI.
III. Lan-
guage, — as
a source of
Error.
Has mail
invented
Language r
Ambiguity
of the
question.
In what
sense Lan-
guage is
natural to
In my last Lecture, I concluded the survey of the
Errors which have their origin in the conditions and
circumstances of the several Cognitive Faculties, and
now proceed to that source of false judgment, which
lies in the imperfection of the Instrument of Thought
and Communication, — I mean Language.
Much controversy has arisen in regard to the ques-
tion, — Has man invented Language "? But the differ-
ences of opinion have in a great measure arisen from
the ambiguity or complexity of the terms, in which
the problem has been stated. By language we may
mean either the power which man possesses of associ-
ating his thought with signs, or the particular systems
of signs with which different portions of mankind
have actually so associated their thoughts.
Taking language in the former sense, it is a natural
faculty, an original tendency of mind, and, in this
view, man has no more invented language than he
has invented thought. In fact, the power of thought
and the power of language are equally entitled to be
LECTURES ON LOGIC. 141
considered as elementary qualities of intelligence ; for lect.
while tliey are so different that they cannot be identi- ' ^ ^ '
fied, they are still so reciprocally necessary that the
one cannot exist without the other. It is true, in-
deed, that presentations and representations of given
individual objects might have taken place, although
there were no signs with which they were mentally
connected, and by which they could be overtly ex-
pressed ; but all complex and factitious constructions
out of these given individual objects, in other words,
all notions, concepts, general ideas, or thoughts proper,
would have been impossible without an association to
certain signs, by which their scattered elements might
be combined in unity, and their vague and evanescent
existence obtain a kind of definite and fixed and
palpable reality. Speech and cogitation are thus the
relative conditions of each other's activity, and both
concur to the accomj^lisliment of the same joint result.
The Faculty of Thinking, — the Faculty of forming
General Notions, — being given, this necessarily tends to
energy, but the energy of thinking depends upon the
coactivity of the Faculty of Speech, which itself tends
equally to energy. These faculties, — these tendencies,
— these energies, thus coexist and have always co-
existed ; and the result of their combined action is
thought in language, and language in thought. So
much for the origin of Language, considered in general
as a faculty.
But, though the Faculty of Speech be natural and wasti.e
1 . . « . . first lan-
necessary, that its manitestations are to a certam ex- guage,
tent contingent and artificial, is evident from the spoken,
simple fact, that there are more than a single language tion of man
or au in-
actually spoken. It may, therefore, be asked, — Was the spiration of
first language, actually spoken, the invention of man, "^ ''' ^ '
142
LECTURES ON LOGIC.
LECT.
XXXI.
The Latter
hypothesis
cousidered.
Difficulty
of the
question.
Language
has a gen-
eral and a
special
character.
or an inspiration of the Deity 1 The latter hypothesis
cuts, but does not loose, the knot. It declares that
ordinary causes and the laws of nature are insufficient
to explain the phcenomenon, but it does not' prove
this insufficiency ; it thus violates the rule of Parci-
mony, by postulating a second and hypothetical cause
to explain an effect, which it is not shown cannot be
accounted for without this violent assumption. The
first and greatest difficulty in the question is thus : —
It is necessary to think in order to invent a language,
and the invention of a language is necessary in order
to think ; for we cannot think without notions, and
notions are only fixed by words." This can only be
solved, as I have said, by the natural attraction be-
tween thought and speech, — by their secret affinity,
which is such that they suggest and, pari ixissu,
accompany each other. And in regard to the ques-
tion, — Why, if speech be a natural faculty, it does not
manifest itself like other natural principles in a uniform
manner, — it may be answered that the Faculty of
Speech is controlled and modified in its exercise by
external circumstances, in consequence of which,
though its exertion be natural and necessary, and,
therefore, identical in all men, the special forms of
decree conventional and
its exertion are m a
great
contingent, and, therefore, different among different
portions of mankind.
Considered on one side, languages are the results of
our intellio:ence and its immutable laws. In conse-
quence of this, they exhibit in their progress and de-
o See Rousseau, Discours sur V Ori- prendre Ji penser, ils out eu bien plus
gine de rhiegalite iMrmi les Ilommes. besoin encore de savoir penser pour
Premiere Partie. " Si les hommes trouver I'art de la parole." — Ed.
out eu besoin de la parole pour ap-
LECTURES ON LOGIC. 1^3
velopment resemblances and common characters which lect.
• • X\XI
allow us to compare and to recall them to certain pri- " " ' '
mitive and essential forms, — to evolve a system of
Universal Grammar. Considered on another side, each
language is the offspring of particular wants, of special
circumstances, physical and moral, and of chance.
Hence it is that every language has particular forms
as it has peculiar words. Language thus bears the
impress of human intelligence only in its general
outlines. There is, therefore, to be found reason and
philosophy in all languages, but w^e should be wrong
in believing that reason and philosophy have, in any
language, determined everything. No tongue, how per- No lau-
fect soever it may appear, is a complete and perfect perfect
mstrument oi human thought, rrom its very condi- of thought,
tions every language must be imperfect. The human
memory can only compass a limited complement of
words, but the data of sense, and still more the com-
binations of the understanding, are wholly unlimited
in number. No language can, therefore, be adequate
to the ends for which it exists ; all are imperfect, but
some are far less incompetent instruments than others.
From what has now been said, you will be pre-
pared to find in Language one of the principal sources
of Error ; but before I go on to consider the particular
modes in which the Imperfections of Language are the
causes of false judgments, — I shall comprise the gen-
eral doctrine in the following paragraph.
H CIV. As the human mind necessarily re- Par. civ.
quires the aid of signs to elaborate, to fix, and — Ts^"*^''
to communicate its notions, and as Articulate Error.
Sounds are the species of signs which most
effectually afford this aid, Speech is, therefore, an
144 LECTURES ON LOGIC.
LECT. indispensable instrument in the hio;lier functions
XXXI
. — 1-!- of thought and knowledge. But as speech is a
necessary, but not a perfect, instrument ; its
imperfection must react upon the mind. For the
Multitude of Languages, the Difficulty of their
Acquisition, their necessary Inadequacy, and the
consequent Ambiguity of Words, both singly
and in combination, — these are all copious sources
of Illusion and Error.«
Expiica- We have already sufficiently considered the reason
Sign's neces- why tliouglit is dependent upon some system of signs
internal or symbols, both for its internal perfection and ex-
of Thought, ternal expression./^ The analyses and syntheses, — the
decompositions and compositions, — in a word, the ela-
borations, performed by the Understanding upon the
objects presented by External Perception and Self-
Consciousness, and represented by Imagination, —
these operations are faint and fugitive, and would have
no existence, even for the conscious mind, beyond the
moment of present consciousness, were we not able to
connect, to ratify, and to fix them, by giving to their
parts, (which would otherwise immediately faU asun-
der), a permanent unity, by associating them with a
sensible symbol, which we may always recall at plea-
sure, and which, when recalled, recalls along with it
the characters which concur in constituting a notion
or factitious object of intelligence. So far signs are
necessary for the internal operation of thought itself.
aKrug, Logik,%li5. — Ed. [Of. Er- §109. Caro, Logique, Part. i. ch. i.
nesti,JnitiaI)octri7iceSolicUoris: Pars art. 9, p. 121. Crousaz, Toussaint.]
Altera; Dialectica, c. 2,% 2i. Wytten- [Crousaz, Logique, t. iii. part i. sect.
bach, Prwcejita Phil. Log. P. iii. c. iii. iii. c. 2, p. 68 et seq. Toussaint, De la
p. 98. Tittel, Logik, p. 292. Kirwaii, Pcnscc. Chs. viii. x. Ed.]
Logick, i. 214. Fiiea, Si/st,an der Logik, ^ See above, vol. i. p. 137. — Ed.
LECTUKES ON LOGIC. 145
But for the communication, of tliouo-ht from one mind lect.
XXXI.
to another, signs are equally indispensable. For in ' ' '
itself thought is known, — thought is knowable, onlyihe'com-
to the thinking mind itself ; and were we not enabled orxhoigTit.
to connect certain complements of thought to certain
sensible symbols, and by their means to suggest in
other minds those complements of thought of which we
were conscious in ourselves, we should never be able
to communicate to others what engaged our interest,
and man would remain for man, if an intelligence at
all, a mere isolated intelligence.
In regard to the question, — What may these sen- lutonations
sible symbols be, by which we are to compass such the only
memorable effects, — it is needless to show that mien sensible
and gesture, which, to a certain extent, afford a kind of thought
of natural expression, are altogether inadequate to the numication.
double purpose of thought and communication, which
it is here required to accomplish. This double pur-
pose can be effected only by symbols, which express,
through intonations of the voice, what is passing in
the mind. These vocal intonations are either inarti- These m-
culate or articulate. The former are mere sounds or and*^rrtl-^
cries ; and, as such, an expression of the feelings of '''''''^'
which the lower animals are also capable. The latter The latter
. P constitute
constitute words, and these, as the expression oi Language
thoughts or notions, constitute Language Proper or
Speech.'* Speech, as we have said, as the instru- How Lan-
. . . . guage is a
ment of elaboratmoj, fixing, and communicating our source of
Error.
thoughts, is a principal mean of knowledge, and even
the indispensable condition on which depends the ex-
ercise of our higher cognitive faculties. But, at the
same time, in consequence of this very dependence of
thought upon language, inasmuch as language is itself
a Cf. Krug, Lofjik, § 1 45. Anm. — Ed.
VOL. IL K
UQ
LECTURES ON LOGIC.
LECT
XXXI.
The ambi-
guity of
words the
principal
source of
error origi-
nating in
Language.
Two cir-
cumstances
under this
head, wliich
mutually
affect each
other.
not perfect, the understanding is not only restrained
in its operations, and its higher development, conse-
quently, checked, but many occasions are given of
positive error. For, to say nothing of the impedi-
ment presented to the free communication of thought
by the multitude of tongues into which human lan-
guage is divided, in consequence of which all speech
beyond their mother-tongue is incomprehensible to
those who do not make a study of other languages, —
even the accurate learning of a single language is at-
tended with such difficulties, that perhaps there never
yet has been found an individual who was thoroughly
acquainted with all the words and modes of verbal
combination in any single language, — his mother-
tongue even not excepted. But the circumstance of
principal importance is, that, how copious and expres-
sive soever it may be, no language is competent ade-
quately to denote all possible notions, and all possible
relations of notions, and from this necessary poverty
of language in all its different degrees, a certain in-
evitable ambiguity arises, both in the employment
of single words and of words in mutual connection.
As this is the principal source of the error originat-
ing in Language, it will be proper to be a little more
explicit. And here it is expedient to take into ac-
count two circumstances, which mutually affect each
other. The first is, that as the vocabulary of every
language is necessarily finite, it is necessarily disj^ro-
portioned to the multiplicity, not to say infinity, of
thought ; and the second, that the complement of
words in any given language has been always filled
up with terms significant of objects and relations of
the external world, before the want was experienced
LECTUllES ON LOGIC. 147
of words to express the obiects and relations of the lect.
. ^ 1 ^ '' XXXI.
internal.
From the first of these circumstances, considered The voca-
exclusively and by itself, it is manifest that one of every Lan-
1 • T 1 TT 1 1 1 guageneces-
two alternatives must take place. Jidther the words sariiy finite.
f, I 11- 1 • 1 Consequen-
01 a language must each designate only a single ces of this.
notion, — a single fasciculus of thought, — the multitude
of notions not designated being allowed to perish,
never obtaining more than a momentary existence in
the mind of the individual ; or the words of a language
must each be employed to denote a plurality of con-
cepts. In the former case, a small amount of thought
would be expressed, but that precisely and without
ambiguity ; in the latter, a large amount of thought
would be expressed, but that vaguely and equivocally.
Of these alternatives, (each of which has thus its ad-
vantages and disadvantages), — the latter is the one
which has universally been preferred ; and, accord-
ingly, all languages by the same word express a mul-
titude of thoughts, more or less differing from each
other. Now what is the consequence of this "? It is
plain that if a word has more than a single mean-
ing attached to it, when it is employed it cannot of
itself directly and peremptorily suggest any definite
thought ; — all that it can do is vaguely and hypothe-
ticaUy to suggest a variety of different notions ; and
we are obliged from a consideration of the context, —
of the tenor, — of the general analogy, of the discourse,
to surmise, with greater or less assurance, with greater
or less precision, what particular bundle of characters
it was intended to convey. Words, in fact, as Ian- words are
guages are constituted, do nothing more than sug- hints L
gest, — are nothing more than hints ; hints, likewise,
XXXI.
148 LECTURES ON LOGIC.
LECT. which leave the principal part of the process of inter-
pretation to be performed by the mind of the hearer.
In this respect, the effect of words resembles the effect
of an outline or shade of a countenance with which
we are familiar. In both cases, the mind is stimu-
lated to fill up what is only hinted or pointed at.
Thus it is that the function of laoguage is not so much
to infuse knowledge from one intelligence to another,
as to bring two minds into the same train of thinking,
and to confine them to the same track. In this pro-
cedure what is chiefly wonderful, is the rapidity with
which the mind compares the word with its correla-
tions, and, in general, without the slightest effort, de-
cides which among its various meanings is the one
which it is here intended to convey. But how mar-
vellous soever be the ease and velocity of this process
of selection, it cannot always be performed with equal
certainty. Words are often employed with a plural-
ity of meanings ; several of which may quadrate, or
be supposed to quadrate, with the general tenor of the
discourse. Error is thus possible ; and it is also pro-
bable, if we have any prepossession in favour of one
interpretation rather than of another. So copious a
source of error is the ambiguity of language, that a
very large proportion of human controversy has been
concerning the sense in which certain terms should
be understood ; and many disputes have even been
fiercely waged, in consequence of the disputants being
unaware that they agreed in opinion, and only differed
in the meaning they attached to the Avords in which
that opinion was expressed. On this subject I may
refer you to the very amusing and very instructive
treatise of Werenfelsius, entitled De Logomachiis
Eruditorum.
LECTUEES ON LOGIC. 149
" In regard to a remedy for this description of error, lect.
• • . XXXI
— this lies exclusively in a thorough study of the '.
language employed in the communication of ki^ow- ^^™^^y.
ledge, and in an acquaintance with the rules of Criti- fr'i^m^Ean-
cism and Interpretation. The study of languages, s^^s^-
when rationally pursued, is not so unimportant as
many fondly conceive ; for misconceptions most fre-
quently arise solely from an ignorance of words ; and
every language may, in a certain sort, be viewed as a
commentary upon Logic, inasmuch as every language,
in like manner, mirrors in itself the laws of thought.
" In reference to the rules of Criticism and Interpre-
tation, — these especially should be familiar to those
who make a study of the writings of ancient authors,
as these writings have descended to us often in a very
mutilated state, and are composed in languages which
are now dead. How many theological errors, for ex-
ample, have only arisen because the divines were
either ignorant of the principles of Criticism and Iler-
meneutic, or did not properly apply them ! Doctrines
originating in a corrupted lection, or in a figurative
expression, have thus arisen and been keenly defended.
Such errors are best combated by philological weapons ;
for these pull them up along with their roots.
"A thorough knowledge of languages in general
accustoms the mind not to remain satisfied with the
husk, but to penetrate in, even to the kernel. AVith
this knowledge we shall not so easily imagine that we
understand a system, when we only possess the lan-
guage in which it is expressed ; we shaU not conceive
that we truly reason, when we only employ certain
empty words and formulae ; we shall not betray our-
selves into unusual and obscure expressions, under
which our meaning may be easily mistaken ; finall3%
150 LECTURES ON LOGIC.
LECT. we shall not dispute with others about words, when we
XXXI . •
— 1-^ are in fact at one with them in reo;ard to thino;s."a
So much for the errors which originate in Language.
IV. Source As to thc last sourcc of Error which I enumerated,
of Error, —
the Objects — the Objects themselves of our knowledge, — it is
of our
knowledge, hardly necessary to say anything. It is evident that
some matters are obscure and abstruse, while others
are clear and palpable ; and that, consequently, the
probability of error is greater in some studies than it
is in others. But as it is impossible to deliver any
special rules for these cases, different from those which
are given for the Acquisition of Knowledge in gen-
eral, concerning which we are soon to speak, — this
source of error may be, therefore, passed over in
silence.
We have now thus jBnished the consideration of the
various Sources of Error, and —
Par. cv. IF CV. The following rules may be given, as
touching the results of the foregoing discussion, touching
and Reme- thc Causcs aud Eemcdics of our False Judgments.
dies of our ^ _, - ... . .
FaiseJudg- 1 . iLudeavour as lar as possible to obtain a
clear and thorough insight into the laws of the
Understanding, and of the Mental Faculties in
general. Study Logic and Psychology.
2°. Assiduously exercise your mind in the ap-
plication of these laws. Learn to think method-
ically.
3°. Concentrate your attention in the act of
Thinking ; and principally employ the seasons
when the Intellect is alert, the Passions slumber-
ing, and no external causes of distraction at work.
a Krug, Logik, § 157. Anm. — Ed.
ments.
LECTURES ON LOGIC. 151
4°. Carefully eliminate all foreign interests lect.
A.XA.1,
from the objects of your inquiry, and allow your-
selves to be actuated by tlie interest of Truth
alone.
5°. Contrast your various convictions, your
past and present judgments, with each other ;
and admit no conclusion as certain, until it has
been once and again thoroughly examined, and
its correctness ascertained.
6°. Collate your own persuasions with tliose
of others ; attentively listen to and weigh, with-
out prepossession, the judgments formed by
others of the opinions which you yourselves
maintain."
a Cf. Krug, Lorjilc, § 160. Bachmann, Loffik, § 416. — Ed.
]52
LECTURES ON LOGIC.
LECTURE XXXII.
MODIFIED METHODOLOGY.
SECTION I. — OF THE ACQUISITION OF KNOWLEDGE.
L EXPERIENCE. — A. PERSONAL: — OBSERVATION
INDUCTION AND ANALOGY.
LECT.
XXXIL
Means by
which our
knowledge
obtains the
character of
Perfection,
viz. the
Acquisition
and the
Communi-
cation of
Knowledge.
The acqui-
sition of
Knowledge.
Human
Knowledge
of two
kinds.
In our last Lecture, having concluded the Second
Department of Concrete Logic, — that which treats of
the Causes of Error, — we now enter upon the Third
part of Concrete or Modified Logic, — that which con-
siders the Means by which our Knowledge obtains the
character of Perfection. These means may, in gen-
eral, be regarded as two, — the Acquisition and the
Communication of knowledge, — and these two means
we shall, accordingly, consider consecutively and apart.
In regard to the Acquisition of Knowledge, — we
must consider this by reference to the difterent kinds
of knowledge of which the human intellect is capable.
And this, viewed in its greatest universality, is of two
species.
Human knowledge, I say, viewed in its greatest
universality, is of two kinds. For either it is one of
which the objects are given as contingent phsenomena ;
or one in which the objects are given as necessary
facts or laws. In the former case, the cognitions are
LECTURES ON LOGIC. 153
called empirical, experiential, or of exp)erience ; in the lect.
latter, pure, intuitive, ratio7ial, or of reason, also of — I — 1
common sense. These two kinds of knowledge are,
likewise, severally denominated cognitions a ^oosteinori
and cognitions a priori. The distinction of these two
species of cognitions consists properly in this, — that
the former are solely derived from the Presentations
of Sense, External and Internal : whereas the latter,
though first manifested on the occasion of such Pre-
sentations, are not, however, mere products of Sense ;
on the contrary, they are laws, principles, forms, no-
tions, or by whatever name they may be called, native
and original to the mind, that is, founded in, or con-
stituting the very nature of. Intelligence ; and, ac-
cordingly, out of the mind itself they must be deve-
loped, and not sought for and acquired as foreign and
accidental acquisitions. As the Presentative Facul-
ties inform us only of what exists and what happens,
that is, only of facts and events, — such empirical
knowledge constitutes no necessary and universal
judgment ; all, in this case, is contingent and particu-
lar, for even our generalised knowledge has only a
relative and precarious universality. The cognitions,
on the other hand, which are given as Laws of Mind,
are, at once and in themselves, universal and neces-
sary. We cannot but think them, if we think at all.
The doctrine, therefore, of the Acquisition of Ilnow- Doctrine of
ledge, must consist of tw^o parts,- — the first treating ofsidonoT"
the acquisition of knowledge through the data of Ex- consists'^ o!^
perience, the second, of the acquisition of knowledge ^''^ ^"''^''"
through the data of Intelligence."
a See Esser, Logik, § 145 Ed. called acquired, inasmuch as it is ac-
In regard to the acquisition of quired either, 1 °, By experience ; or,
knowledge, — all knowledge may be 2°, On occasion of experience.
15-t LECTURES ON LOGIC.
LECT. In reo-ard to the first of these sources, viz. Experi-
XXXII . .
—1 — '- ence, — this is either our own experience or the expe-
tri Je' of^x- ^i^iic® of others, and in either case it is for us a mean
ExpeH^nce ^f kuowledgc. It is manifest that the knowledge we
kinds! acquire through our personal experience, is far supe-
rior in degree to that which we obtain through the
experience of other men ; inasmuch as our knowledge
of an object, in the former case, is far clearer and more
distinct, far more complete and lively, than in the
latter ; while at the same time the latter also affords
us a far inferior conviction of the correctness and cer-
tainty of the cognition than the former. On the
other hand, foreign is far superior to our proper expe-
rience in this, — that it is much more comprehensive,
and that, without this, man would be deprived of those
branches of knowledge which are to him of the most
indispensable importance. Now, as the principal dis-
tinction of experience is thus into our own experience
and into the experience of others, we must consider it
more closely in this twofold relation.^ First, then, of
our Personal Experience,
1. Personal Experience necessarily supposes, as its primary con-
dition, certain presentations by the faculties of Ex-
ternal or of Internal Perception, and is, therefore, of
two kinds, according as it is conversant about the
objects of the one of these faculties, or the objects of
the other. But the presentation of a fact of the ex-
ternal or of the internal world is not at once an expe-
rience. To this there is required, a continued series
of such presentations, a comparison of these to-
gether, a mental separation of the different, a mental
combination of the similar, and it, therefore, over and
above the operation of the Presentative Faculties, re-
a Esser, Lor/ik, § 146. — Ed.
LECTURES ON LOGIC. 155
quires the co-operation of the Retentive, the Repro- lect.
• • . XXXII
ductive, the Representative, and the Elaborative — ^ — 1
Faculties. In regard to Experience, as the first means
by which we acquire knowledge through the legiti-
mate use and application of our Cognitive Faculties,
I give you the following paragraph : —
H CVI. The First Mean towards the Acquisi- Par. cvi.
tion of Knowledge is Experience (ex]jerieiitia,^Alt^—^n'
ilxTTeipia). Experience may be, rudely and gener- ^^^^^ '
ally, described as the apprehension of the phse-
nomena of the outer world, presented by the
Faculty of External Perception, and of the
phsenomena of the inner world, presented by the
Faculty of Self-consciousness : — these phaenomena
being retained in Memory, ready for Reproduc-
tion and Representation, being also arranged into
order by the Understanding.
This paragraph, you will remark, affords only aExpiica-
preliminary view of the general conditions of Expe-
rience. In the first place, it is evident, that without
the Presentative, or, as they may with equal propriety
be called, the Acquisitive, Faculties of Perception,
External and Internal, no experience would be pos-
sible. But these faculties, though affording the fun-
damental condition of knowledge, do not of themselves
make up experience. There is, moreover, required
of the phsenomena or appearances the accumulation
and retention, the reproduction and representation.
Memory, Reminiscence, and Imagination must, there-
fore, also co-operate. Finally, unless the phsenomena
be compared together, and be arranged into classes,
according to their similarities and differences, it is
156 LECTURES ON LOGIC.
LFXT. evident that no iuclefments, — no conclusions, can be
XXXII .
1 formed concerning tliem ; but without a judgment
knowledge is impossible ; and as experience is a know-
ledge, consequently experience is impossible. The
Understanding or Elaborative Faculty must, there-
fore, likewise co-operate. Manilius has well expressed
the nature of experience in the following lines : —
" Per varies usus artem experientia fecit,
Exemplo monstrante viam," "
And Afranius in the others : —
" Usus me geuuit, mater peperit Meraoria ;
Sophiam vocant me Graii, vos Sapientiam,";3
Common " Our owu obscrvation, be it external or internal, is
and Scien- , . .
tificEspe- either with, or without, intention ; and it consists
rieuce.
either of a series of Presentations alone, or Abstrac-
tion and Keflection supervene, so that the presenta-
tions obtain that completion and system which they
do not of themselves possess. In the former case, the
experience may be called an Unlearned or a Common;
in the latter, a Learned ox Scientific Experience. In-
tentional and reflective experience is called Ohser-
observa- vatiou. Observation is of two kinds ; for either the
what. objects which it considers remain unchanged, or, pre-
kinds,— vious to its application, they are made to undergo
Observation . , . , i i •
Proper, and ccrtaiu arbitrary changes, or are placed in certain
nient. factitious rclatious. In the latter case, the observation
obtains the specific name of Eocperiment. Observation
and Experiment do not, therefore, constitute opposite
or two different procedures, — the latter is, in propriety,
only a certain subordinate modification of the former;
for, while observation may accomplish its end without
o I. 61. f^is Poetarnm Lat'moruni, vol. ii. p.
/3 Frarjmcntmn e Sella. Vide Cor- ISl.'?, Lond. 1713.— Ed.
LECTURES ON LOGIC. 157
experiment, experiment without observation is impos- lect.
sible. Observation and experiment are manifestly __U__
exclusively competent upon the objects of our empiri-
cal knowledge ; and they co-operate, equally and in
like manner, to the progress of that knowledge, partly
by establishing, partly by correcting, partly by ampli-
fying it. Under observation, therefore, is not to be
understood a common or unlearned experience, which
obtrudes itself upon every one endowed with the ordi-
nary faculties of Sense and Understanding, but an
intentional and continued application of the faculties
of Perception, combined with an abstractive and re-
flective attention to an object or class of objects, a
more accurate knowledge of which, it is proposed, by
the observation, to accomplish. But in order that the Pr»cognita
observation should accomplish this end, — more espe- tion. *^"'^
cially when the objects are numerous, and a systematic
complement of cognitions is the end proposed, — it is
necessary that we should know certain prsecognita, —
1°. What we ought to observe ; 2°. How we ought
to observe ; and 3°. By what means are the data of
observation to be reduced to system. The fii'st of
these concerns the Object; the second, the Procedure;
the third, the scientific Completion, of the observa-
tions. It is proper to make some general observa-
tions in regard to these, in their order ; and first,
of the Object of observation, — the ivliat we ought to
observe.
" The Object of Observation can only be some given First,— The
and determinate phsenomenon, and this phsenomenon obiefva-
either an external or an internal. Through obser-
vation, whether external or internal, there are four This four-
several cognitions which we propose to compass, — viz.,
to ascertain — 1°. What the Phoenomena themselves
158 LECTURES ON LOGIC.
LECT. are ; 2°. What are tlie Conditions of tlieir Reality ;
L 3°. Wliat are the Causes of their Existence ; 4°. What
is the Order of their Consecution.
1°. What " In regard to what the phsenomena themselves
nomenaare. are {quid siiit), that is, in regard to what constitutes
their peculiar nature, — this, it is evident, must be the
primary matter of consideration, it being always sup-
posed that the fact (the an sit) of the phsenomenon
itself has been established.'* To this there is required,
In their abovc all, a clear and distinct Presentation or Repre-
pVuTiarHies scutatiou of thc objcct. lu ordcr to obtain this, it
trastsr' behoves us to analyse, — to dismember, the constituent
parts of the object, and to take into proximate ac-
count those characters which constitute the object,
that is, which make it to be what it is, and nothing
but what it is. This being performed, we must pro-
ceed to compare it with other objects, and with those
especially which bear to it the strongest similarity,
taking accurate note always of those points in which
they reciprocally resemble, and in which they recipro-
cally disagree.
As under " But it is not euougli to consider the several phse-
geS anT Homcna in their individual peculiarities and contrasts,
species. — ^^ what they are and in what they are not, — it is
also requisite to bring them under determinate genera
and species. To this end we must, having obtained
(as previously prescribed) a clear and distinct know-
ledge of the several phaenomena in their essential
similarities and differences, look away or abstract
from the latter, — the differences, and comprehend the
former, — the similarities, in a compendious and char-
acteristic notion, under an appropriate name.
a Better the Aristotelic questions, p/iys/cs, vol. i. p. 56. — Ed.]
- A n Sit, &c. [See Lectures on Mcta-
LECTURES ON LOGIC. 159
" When the distinctive peculiarities of the phse- lect.
XXXII
nomena have been thus defiuitively recognised, the 1
second question emerges, — What are the Conditions ^^"^ what^
of their Reality. These conditions are commonly {[°°^.°f^^*^''^
called Requisites, and under requisite we must un-
derstand all that must have preceded, before the
phaenomena could follow. In order to discover the
requisites, we take a number of analogous cases, or
cases similar in kind, and inquire what are the cir-
cumstances under which the phsenomenon always
arises, if it does arise, and what are the circumstances
under which it never arises ; and then, after a com-
petent observation of individual cases, we construct
the general judgment, that the phsenomenon never
occurs unless this or that other phsenomenon has pre-
ceded, or at least accompanied, it. Here, however, it
must be noticed, that nothing can be viewed as a requi- 3°. AVhat
site wdiich admits of any, even the smallest, exception. orthe'^Pha-
" The requisite conditions being discovered, the ^^^^^^'
third question arises, — What are the Causes of the
Phsenomena. According to the current doctrine, the
causes of phoenomena are not to be confounded with
their requisites ; for although a phsenomenon no more
occurs without its requisite than without its cause,
still, the requisite being given, the phsenomenon does
not necessarily follow, and, indeed, very frequently
does not ensue. On the contrary, if the cause occurs,
the phsenomenon must occur also. In other words,
the requisite or condition is that without which the
phsenomenon never is ; the cause, on the other hand,
is that through which it always is. Thus an emotion
of pity never arises without a knowledge of the mis-
fortune of another ; but so little does this knowledge
necessitate that emotion, that its opposite, a feeling
1()0 LECTURES OX LOGIC.
LECT. of rejoicii]g, complacency, at sucli suffering may ensue;
'- whereas the knowledo-e of another's misfortune must
be followed by a sentiment of pity, if we are predis-
posed in favour of the person to whom the misfortune
has occurred. In this view, the knowledge of another's
misfortune is only a requisite ; whereas our favour-
able predisposition constitutes the cause. It must,
however, be admitted, that in different relations one
and the same circumstance may be both requisite and
cause ;"" and, in point of fact, it would be more cor-
rect to consider the cause as the whole sum of ante-
cedents, without which the ph?enomenon never does
take place, and with which it always must. What
are commonly called requisites, are thus, in truth, only
partial causes ; what are called causes, only proximate
requisites.
4°. What " In the fourth place, having ascertained the essen-
their Con- tial qualitics — the Conditions and the Causes of phe-
nomena — a final question emerges, — AVhat is the Order
in which they are manifested 'I and this being ascer-
tained, the observation has accomplished its end. This
question applies either to a phsenomenon considered
in itself, or to a phsenomenon considered in relation
to others. In relation to itself the question concerns
only the time of its origin, of its continuance, and of
its termination ; in relation to others, it concerns the
reciprocal consecution in which the several phseno-
mena appear."^
SecoiKi,— " We now go on to the Second Prsecognitum, — the
of obser'"a-' Mauucr of Obscrvatiou, — How we are to observe.
What we have hitherto spoken of, — the Object, — can
be known only in one way, — the way of Scientific
Observation. It, therefore, remains to be asked, —
a Esser, Lor/!/.: § 148.— Ed. i8 //;/(/.
LECTURES ON LOGIC. 161
How must the observation be instituted, so as to lect.
afford us a satisfactory result in regard to all the four —^ — -
sides on which it behoves an object to be observed 1 state oUhe
In the first place, as preliminary to observation, it iSmiuT""
required that the observing mind be tranquil and
composed, be exempt from prejudice, partiality, and
prepossession, and be actuated by no other interest
than the discovery of truth. Tranquillity and com-
posure of mind are of peculiar importance in our ob-
servation of the phsenomena of the internal world ;
for these phsenomena are not, like those of the exter-
nal, perceptible by sense, enclosed in space, continu-
ous and divisible ; and they follow each other in such
numbers, and with such a rapidity, that they are at
best observable with difficulty, often losing even their
existence by the interference of the observing, — the re-
flective energy, itself. But that the observation should
be always conducted in the calm and collected state
of mind required to purify this condition, we must
be careful to obtain, more and more, a mastery over
the Attention, so as to turn it with full force upon a
single aspect of the phronomena, and, consequently,
to abstract it altogether from every other. Its proper
function is to contemplate the objects of observation
tranquilly, continuously, and without anxiety for the
result ; and this, likewise, without too intense an
activity or too vigorous an application of its forces.
But the observation and concomitant energy of atten- 2°. Condi-
tion will be without result, unless we previously well questLi to
consider what precise object or objects we are now to mineVby
observe. Nor will our ex^^erience obtain an answer to ation. *^'^^'
the question proposed for it to solve, unless that ques-
tion be of such a nature as will animate the observing
faculties by some stimulus, and give them a determi-
VOL. IL L
1G2 LECTURES ON LOGIC.
LECT. nate direction. Wliere this is not the case, attention
1 1 does not effect anything, nay, it does not operate at
all. On this account such psychological questions as
the following : What takes place in the process of
Self- consciousness, — of Perception, — of Vision, — of
Hearing, — of Imagination, &c., — cannot be answered,
as thus absolutely stated, that is, without reference to
some determinate object. But if I propose the pro-
blem, — What takes place when I see this or that
object, or better still, when I see this table, — the atten-
tion is stimulated and directed, and even a child can
give responses, which, if properly illustrated and ex-
plained, will afford a solution to the problem. If,
therefore, the question upon the object of observation
be too vague and general, so that the attention is not
suitably excited and applied, — this question must be
divided and subdivided into others more particular,
and this process must be continued until we reach a
question which affords the requisite conditions. We
should, therefore, determine as closely as possible the
object itself, and the phases in which we wish to ob-
serve it, separate from it all foreign or adventitious
parts, resolve every question into its constituent ele-
ments, enunciate each of these as specially as possible,
and never couch it in vague and general expressions.
But here we must at the same time take care, that the
object be not so torn and mangled, that the attention
feels no longer any attraction to the several parts, or
that the several parts can no longer be viewed in their
natural connection. So much it is possible to say in
general, touching the Manner in which observation
ought to be carried on ; what may further be added
under this head, depends upon the particular nature
of the objects to be observed.""
a Esser, Lofjil; § 149.— Ed.
LECTURES ON LOGIC. 168
" In this manner, then, must we proceed, until all lect.
has been accomplislied which the problem, to be an-
swered by the observation, pointed out. When the
observation is concluded, an accurate record or nota-
tion of what has been observed is of use, in order to
enable us to supply what is found wanting in our sub-
sequent observation. If we have accumulated a con-
siderable apparatus of results, in relation to the object
we observe, it is proper to take a survey of these :
from what is found defective, new questions must be
evolved ; and an answer to these sought out through
new observations. When the inquiry has attained
its issue, a tabular view of all the observations made
upon the subject is convenient, to afford a conspectus
of the whole, and as an aid to the memory. But how. Third,—
(and this is the Third Precognition), individual ob-bywhrch**
servations are to be built up into a systematic whole, observatron
is to be sought for partly from the nature of science in Suce^to
general, partly from the nature of the particular em- ^J'^*^™-
pirical science for the constitution of which the ob-
servation is applied. Nor is what is thus sought
difhcult to find. It is at once evident, that a syn-
thetic arrangement is least applicable in the empirical
sciences. For, anterior to observation, the object is
absolutely unknown ; and it is only through observa-
tion that it becomes a matter of science. We can,
therefore, only go to work in a problematic or inter-
rogative manner, and it is impossible to commence by
assertory propositions, of which we afterwards lead
the demonstration. We must, therefore, determine
the object on aU sides, in so far as observation is com-
petent to this ; we must analyse every question into
its subordinate questions, and each of these must find
its answer in observation. The systematic order is
thus given naturally and of itself ; and in this pro-
164 LECTURES ON LOGIC.
LECT. cedure it is impossible that it sliould not be given.
L But for a comprehensive and all-sided system of em-
pirical knowledge, it is not sufficient to possess the
whole data of observation, to have collected these to-
gether, and to have arranged them according to some
external principle ; it is, likewise, requisite that we
have a thorough-going principle of explanation, even
though this explanation be impossible in the way of
observation, and a power of judging of the data, ac-
cording to universal laws, although these universal
laws may not be discovered by experience alone.
These two ends are accomplished by different means.
The former we compass by the aid of Hypothesis, the
latter, by the aid of Induction and Analogy."" Of
these in detail. In regard to Hypothesis, I give you
the following paragraph.
Par. cvii. H CVII. When a phaonomenon is presented,
- what. ' which can be explained by no principle afforded
through Experience, we feel discontented and un-
easy; and there arises an effort to discover some
cause which may, at least provisorily, account
for the outstanding phasnomenon : and this cause
is finally recognised as valid and true, if, through
it, the given phccnomenon is found to obtain a
full and perfect explanation. The judgment in
which a phsenomenon is referred to such a pro-
blematic cause, is called an Hi/j^othe^is/
Expiica- Hypotheses have thus no other end than to satisfy
tion
Hypothesis, the desire of the mind to reduce tlie oljjects of its
— its end.
a 'Eascr, Loffik, % ] 50. — Ed. hires on Metaphysics, vol. i. p. 168
)8 Esser, Lurj'd; § 151. Cf. Lee- et seq. — Ed.
LECTURES ON LOGIC. 165
knowledge to unity and system ; and tliey do this in lect.
recalling them, ad interim, to some principle, through — ^ — '-
which the mind is enabled to comprehend them. From
this view of their nature, it is manifest how far they
are j^ermissible, and how far they are even useful and
expedient ; throwing altogether out of account the
possibility, that what is at first assumed as hypothet-
ical, may, subsequently, be proved true.
When our experience has revealed to us a certain
correspondence among a number of objects, we are
determined, by an original principle of our nature, to
suppose the existence of a more extensive correspond-
ence than our observation has already proved, or may
ever be able to establish. This tendency to generalise
our knowledge by the judgment, — that where much
has been found accordant, all will be found accordant,
— is not properly a conclusion deduced from premises,
but an original principle of our nature, which we may
call that of Logical, or perhaps better, that of Philo-
sophical, Pi'esumj^tion. This Presumption is of two
kinds ; it is either Induction or Analogy, which, though
usually confounded, are, however, to be carefully dis-
tinguished. I shall commence the consideration of
these by the following paragraph.
IF CVIII. If we have uniformly observed, that Par. cyin.
a number of objects of the same class (genus or and Ana-
species) possess in common a certain attribute,
we are disposed to conclude that this attribute is
possessed by all the objects of that class. This
conclusion is properly called an htference of
Induction. Again, if we have observed that two
or more things asjree in several internal and
166 LECTURES ON LOGIC.
LECT. essential characters, we are disposed to conclude
L that they agree, likewise, in all other essential
characters, that is, that they are constituents of
the same class (genus or species). This conclu-
sion is properly called an Inference of Analogy.
The principle by which, in either case, we are
disposed to extend our inferences beyond the
limits of our experience, is a natural or ultimate
principle of intelligence ; and may be called the
principle of Logical, or, more properly, of Philo-
sophical, Presumption.^
Expiica- " The reasoning by Induction and the reasoning by
Induction Analogy have this in common, that they both conclude
fJy,J?their from something observed to something not observed ;
ami^dT&r- from somcthiug within to something beyond the sphere
^^'^^' of actual experience. They differ, however, in this,
that, in Induction, that which is observed and from
which the inference is drawn to that which is not ob-
served, is a unity in plurality : whereas, in Analogy,
it is a plurality in unity. In other words, in Induc-
tion, we look to the one in the many ; in Analogy we
look to the many in the one : and while in both we
conclude to the unity in totality, we do this, in Induc-
tion, from the recognised unity in plurality, in Analogy,
from the recognised plurality in unity. Thus, as induc-
tion rests upon the principle, that what belongs, (or does
not belong), to many things of the same kind, belongs,
(or does not belong), to all things of the same kind ;
so analogy rests upon the principle, — that things which
have many observed attributes in common, have other
a Cf. Esser, Lorjih, §§ 140, 152. Systema Lorjicum, §§ 572, 573. Nuii-
Kriig, Lorjik, §§ 166, 167, 168. — Ed. nesius, Dc Constitullone Artis Dia-
[W o\i, Phil. Rat ionalis, § 479. Reusch, Iccticw, p. 126.]
LECTURES ON LOGIC. 167
not observed attributes in common likewise."" It is lect.
XXXII
hardly necessary to remark that we are now speaking
of Induction and Analogy, not as principles of Pure
Logic, and as necessitated by the fundamental laws
of thought, but of these as means of acquiring know-
ledge, and as legitimated by the conditions of objective
reality. In Pure Logic, Analogy has no place, and
only that induction is admitted, in which all the
several parts are supposed to legitimate the inference
to the whole. Aj^j^lied Induction, on the contrary,
rests on the constancy, — the uniformity, of nature,
and on the instinctive expectation we have of this
stability. This constitutes what has been called the
principle of Logical Presumption, though perhaps it
might, with greater propriety, be called the principle
of Philosophical Presumption. We shall now con-
sider these severally ; and, first, of Induction.
An Induction is the enumeration of the parts, in induction,
order to legitimate a judgment in regard to the
whole." Now, the parts may either be individuals or
particulars strictly so called. I say strictly so called,
for you are aware that the term particular is very
commonly employed, not only to denote the species, as
contained under a genus, but, likewise, to denote the
individual, as contained under a species. Using, how-
ever, the two terms in their proper significations, I
say, if the parts are individual or singular things, the
induction is then cdXl^di I aclividual ; whereas if the o; two
parts be species or subaltern genera, the induction individual
then obtains the name of Special. An example of '"' ^"""^
the Individual Induction is given, were we to argue
a Esser, Lorjik, § 152.— Ed. Arabum, p. 36.) Bonnaj, 1836. Zaba-
j8 [Cf. Ah u, All (Avicenncv) Viri ve\\A,Opera Logica,DeNatura Lo(jic(X,
Docti, Be Logica Poema, 1. 190. (In L. i. c. 18, p. 45.]
Schmolders, Bocumenta PMlosopMce
168 LECTURES ON LOGIC.
LECT. tlius, — Mercury, Venus, the Earth, Mars, c&c., are
L bodies in themselves opaque, and ivhich horroiv their
light from the sun. But Mercury, Venus, &c., are
planets. Tlierefore, all planets are opaque, and hor-
roiv their liglvt from the sun. An example of the
special is given, were we argue as follows, — Quadru-
peds, birds, fishes, the amphibia, &c., all have a
nervous system. But quadrupeds, birds, &c., are
animals. Therefore all animals, (tlioiigli it is not yet
detected in some), have a nervous system. Now, liere
it is manifest that Special rests upon Individual in-
duction, and that, in the last result, all induction is
individual. For we can assert nothing concerning
species, unless what we assert of them has been pre-
viously observed in their constituent singulars.a
Twocou- For a legitimate Induction there are requisite at
legitrmate Icast two couditions. In the first place, it is necessary,
That the partial (and this word I use as including both
the terms individual and particular), — I say, it is ne-
cessary that the partial judgments out of which the
total or general judgment is inferred, be all of the
same quality. For if one even of the partial judg-
ments had an opposite quality, the whole induction
would be subverted. Hence it is that we refute uni-
versal judgments founded on an imperfect induction,
by bringing what is called an instance (instantia),
that is, by adducing a thing belonging to the same
class or notion, in reference to which the opposite
holds true. For example, the general assertion. All
dogs bark, is refuted by the instance of the dogs of
Labrador or California (I forget which), — these do not
bark. In like manner, the general assertion. No qua-
druped is oviparous, is refuted by the instance of the
a Krug, Loijil; § 1G7. Anm.— Ed. /3 Esser, Lorjik, § 15-2.— Ed.
luduC'
tion,—
First.
LECTURES ON LOGIC. 109
Ornithorhynchus Paradoxus. But tliat the universal ^^^^
jiiclgment must liave the same quahty as the partial,
is self-evident ; for this judgment is simply the asser-
tion of something to be true of all which is true of
many.
The second condition required is, That a competent Second.
]mmber of the partial objects from which the induc-
tion departs should have been observed, for otherwise
the comprehension of other objects under the total
judgment would be rash." What is the number of
such objects, which amounts to a competent induc-
tion, it is not possible to say in general. In some
cases, the observation of a very few particular or indi-
vidual examples is sufficient to warrant an assertion in
regard to the whole class ; in others, the total judgment
is hardly competent, until our observation has gone
through each of its constituent parts. This distinc-
tion is founded on the difference of essential and un-
essential characters. If the character be essential to
the several objects, a comparatively limited observa-
tion is necessary to legitimate our general conclusion.
For example, it would require a far less induction to
prove that all animals breathe, than to prove that the
mammalia, and the mammalia alone, have lateral
lobes to the cerebellum. For the one is seen to be a
function necessary to animal life ; the other, as far as
our present knowledge reaches, appears only as an
arbitrary concomitant. The difference of essential
and accidental is, however, one itself founded on in-
duction, and varies according to the greater or less
perfection to which this has been carried. In the pro-
gress of science, the lateral lobes of the cerebellum
may appear to future physiologists as necessary a
a Es.ser, Lo(/il-, % 152. — Ed.
170 LECTURES ON LOGIC.
LECT. condition of the function of sucklino; their yonncy, as
XXXTT . . .
1 the organs of breathing appear to us of circulation
and of life.
Summary To suui up tlio Doctriue of luduction, — " This is
doctrine of morc ccrtaiu, 1°, In proportion to the number and
diversity of the objects observed ; — 2°, In proportion
to the accuracy with which the observation and com-
parison have been conducted ; — 3°, In proportion as
the agreement of the objects is clear and precise ; —
and, 4°, In proportion as it has been thoroughly ex-
plored, whether there exist exceptions or not."«
Almost all induction is, however, necessarily imper-
fect ; and Logic can inculcate nothing more import-
ant on the investigators of nature than that sobriety
of mind, which regards all its past observations only
as hypothetically true, only as relatively complete,
and which, consequently, holds the mind open to
every new observation, which may correct and limit its
former judgments.
Analogy,— So much for Inductiou ; now for Analogy. Ana-
logy, in general, means proportion, or a similarity of
relations. Thus, to judge analogically or according to
analogy, is to judge things by the similarity of their
relations. Thus when we judge that as two is to
four, so is eight to sixteen, we judge that they are
analogically identical ; that is, though the sums in
other respects are different, they agree in this, that
as two is the half of four, so eight is the half of
sixteen.
In common language, however, this propriety of
the term is not preserved. For by analogy is not
always meant merely by proportiofi but frequently
by comparison — by relation, or simply by similarity.
a Esser, Logih, § 152.— Ed.
what
LECTURES ON LOGIC. l7l
In so far as Analoo;y constitutes a particular kind of lect.
XXXII
reasoning from the individual or particular to the '-
universal, it signifies an inference from the partial
similarity of two or more things to their complete or
total similarity. For example, — This disease corre-
sponds in many symptoms ivith iJiose we have observed
in typhus fevers ; it ivill, therefore, correspond in all,
that is, it is a typhus fever. '^
Like Induction, Analogy has two essential requi- Has two
sites. In the first place, it is necessary that of two condi-""
or more things a certain number of attributes should F^°st.
have been observed, in order to ground the inference
that they also agree in those other attributes, Tvhich
it has not yet been ascertained that they possess. It
is evident that in proportion to the number of points
observed, in which the things compared together coin-
cide, in the same proportion can it be with safety as-
sumed, that there exists a common principle in these
things, on which depends the similarity in the points
known as in the points unknown.
In the second place, it is required that the predi- second,
cates already observed should neither be all negative
nor all contingent ; but that some at least should be
positive and necessary. Mere negative characters
denote only what the thing is not ; and contingent
characters need not be present in the thing at all. In
regard to negative attributes, the inference, that two
things, to which a number of qualities do not belong,
and which are, consequently, similar to each other only
in a negative point of view, — that these things are,
therefore, absolutely and positively similar, is highly
improbable. But that the judgment in reference to
a Cf. Krug, Zor/yX', § 168. Anm. — '^c\\vao\(}iers, Documenta Phil. Arahum,
Ed. [Condillac, L'Art dc Eaisonner, p. 36.) Whately, Rhetoric, p. 74.]
I L. iv. ch. 3, p. 159. Avicenna, (in
172
LECTURES ON LOGIC.
LECT.
XXXII.
Summary
of the
doctrine of
Analogy,
Induction
and Ana-
logy com-
pared to-
gether.
the compared things (say A and X) must be of the
same quality {i.e. either both affirmative or both nega-
tive), is self-evident. For if it be said A is B, X is
not B, A is not G, 'X. is C ; their harmony or simi-
larity is subverted, and we should rather be war-
ranted in arguing their discord and dissimilarity in
other points. And here it is to be noticed that Ana-
logy differs from Induction in this, that it is not
limited to one quality, but that it admits of a mix-
ture of both.
In regard to contingent attributes, it is equally
manifest that the analogy cannot proceed exclusively
upon them. For, if two things coincide in certain
accidental attributes (for example, two men in respect
of stature, age, and dress), the supposition that there
is a common principle, and a general similarity
founded thereon, is very unlikely.
To conclude : Analogy is certain in proportion,
1°, To the number of congruent observations ; 2°, To
the number of congruent characters observed ; 3°, To
the importance of these characters and their essenti-
ality to the objects; and, 4°, To the certainty that the
characters really belong to the objects, and that a
partial correspondence exists.* Like Induction, Ana-
logy can only pretend at best to a high degree of
probability ; it may have a high degree of certainty,
but it never reaches to necessity.
Comparing these two processes together : — " The
Analogical is distinguished from the Inductive in this
— that Induction regards a single predicate in many
subjects as the attribute Z in A, in B, in C, in D,
in E, in F, &c. ; and as these many belong to one
class, say Q ; it is inferred that Z will, likewise, be
a Esser, Lofjlk, § 152. Cf. Krug, Loffik, § 168. Anm. — Ed.
LECTURES ON LOGIC. 173
met witli in the otlier things belongino; to this class, lect.
XXXII
that is, in all Qs. On the other hand. Analogy re- 111 — 1
gards many attributes in one subject (say m, 7i, o, p,
in A) ; and as these many are in part found in
another subject (say m, and n, in B), it is concluded
that, in that second thing, there will also be found the
other attributes (say o and p). Through Induction
we, therefore, endeavour to prove that one character
belongs, (or does not belong), to all the things of a
certain class, because it belongs, (or does not belong), to
many things of that class. Through Analogy, on the
otlier hand, we seek to prove that all the characters
of a thing belong, (or do not belong), to another or
several others, because many of these characters be-
long to this other or these others. In the one it is
proclaimed, — One in many, therefore one in all. — In
the other it is proclaimed, — Many in one, therefore all
in one!'^
" By these processes of Induction and Analogy, as luductiou
observed, we are unable to attain absolute certainty ; iog>- do not
—a great probability is all that we can reach, and lute eer-
this for the simple reason, that it is impossible,
under any condition, to infer the unobserved from
the observed,— the whole from any proportion of the
parts, — in the way of any rational necessity. Even
from the requisites of Induction and Analogy, it is
manifest that they bear the stamp of uncertainty ;
inasmuch as they are unable to determine how many
objects or how many characters must be observed, in
order to draw the conclusion that the case is the same
with all the other objects, or with all the other char-
acters. It is possible only in one way to raise Induc-
tion and Analogy from mere probability to complete
o Krug, Lmjik, § 168. Anm. — Ed.
XXXII
174 LECTURES ON LOGIC.
LECT. certainty, — viz. to demonstrate that the principles
which lie at the root of these processes, and which
we have already stated, are either necessary laws of
thought, or necessary laws of nature. To demonstrate
that they are necessary laws of thought is impossible ;
for Logic not only does not allow inference from
many to all, but expressly rejects it. Again, to de-
monstrate that they are necessary laws of nature is
equally impossible. This has indeed been attempted,
from the uniformity of nature, but in vain. For it is
incompetent to evince the necessity of the inference of
Induction and Analogy from the fact denominated
the laiv of nature ; seeing that this law itself can only
be discovered by the way of Induction and Analogy.
In this attempted demonstration there is thus the
most glaring j^eiii^o ^97*Z7^cipiV. The result which has
been previously given remains, therefore, intact : —
Induction and Analogy guarantee no perfect cer-
tainty, but only a high degree of probability, while all
probability rests at best upon Induction and Analogy,
and nothing else.""
a Esser, LogiJc, §152. — Ed. [On et seq. lIoSha,\ier,A7ifaiigsffru7ideder
history and doctrine of the Logic of Lor/ik, § 422 et seq. Bolzano, Loyih,
Probabilities, see Leibnitz, Nov.veaux vol. ii. § 161, vol. iii, § 317. Bachmann,
Essais, L. iv. ch. xv. p. 425, ed. Raspe. Logil:, § 229 et seq. Fries, Lo<jik, §
Wolf, Phil. Rat. § 564 et seq. Platner, 96 et seq. Prevost, Essais de Philo-
Phil. Aphorismen, § 701 (old edit.) § sophie, ii. L. i. part iii. p. 56. Kant,
594 (new edit.) Zedler, Lexikon, v. Logik, Einleitung x. Jacob, Grun-
Wahrschei7ilich.'Wa.lch.,Lexil-on,Jbid. driss der Allgemeinen Logik, § 358,
Lambert, Neues Organon, ii. p. 318 p. 131 et seq., 1800, Halle. Metz,
et seq. Reusch, Systema Logicmn, § Institutiones Logiae, § 230 et seq., p.
653 et seq. Hollmann, Logica, § 215 171, 1796.]
LECTURES ON LOGIC. 175
LECTURE XXXIII.
MODIFIED METHODOLOGY.
SECTION I. — OF THE ACQUISITION OF KNOWLEDGE.
I. EXPERIENCE. B. FOREIGN : ORAL TESTIMONY
— ITS CREDIBILITY.
Having, in our last Lecture, terminated the Doctrine lect.
XXXIII
of Empirical Knowledge, considered as obtained Im-
erience.
mediately — that is, through the exercise of our own Expemi
powers of Observation, — we are now to enter on the
doctrine of Empirical Knowledge, considered as ob-
tained Mediately — that is, through the Experience of
Other Men. The following paragraph will afford you
a general notion of the nature and kinds of this
knowledge : —
II CIX. A matter of Observation or Empiri- Par.cix.
cal Knowledge can only be obtained Mediately,
that is, by one individual from another, through
an enouncement declaring it to be true. This
enouncement is called, in the most extensive sense
of the word, a Witnessing or Testimony, {testimo-
nium) ; and the person by whom it is made is,
in the same sense, called a Witness, or Testijier,
(testis). The object of the Testimony is called
17G
LECTURES ON LOGIC.
LECT.
xxxin.
the Fact, {factum); and its validity constitutes
what is styled Historical Credibility, {credihilitas
historica). To estimate this credibility, it is re-
quisite to consider — 1°, The Subjective Trust-
worthiness of the Witnesses, (Jides testium), and
2°, The Objective Probability of the Fact itself.
The former is founded partly on the Sincerity,
and partly on the Competence, of the Witness.
The latter depends on the Absolute and Eelative
Possibility of the Fact itself. Testimony is either
Immediate or Mediate. Immediate, where the
fact reported is the object of a Personal Expe-
rience ; Mediate, where the fact reported is the
object of a Foreign Experience."
Explica-
tioa.
" It is manifest that Foreign Experience, or the ex-
perience of other men, is astricted to the same laws,
and its certainty measured by the same criteria, as the
experience we carry through ourselves. But the expe-
rience of the individual is limited, when compared
with the experience of the species ; and if men did
not possess the means of communicating to each
other the results of their several observations, — were
they unable to co-operate in accumulating a stock
of knowledge, and in carrying on the progress of dis-
covery, — they would never have risen above the very
lowest steps in the acquisition of science. But to this
mutual communication they are competent; and each
individual is thus able to appropriate to his own
benefit the experience of his fellow-men, and to confer
on them in return the advantages which his own ob-
servations may supply. But it is evident that this reci-
u Krug, Lxjll-, § 172— Ed. [Of. Scheibler, Topkn, c. 31.]
LECTURES ON LOGIC. 177
procal communication of their respective experiences lect.
among men, can only be effected inasmuch as one is "
able to inform another of what he has himself ob-
served, and that the vehicle of this information can
only be some enouncement in conventional signs of
one character or another. The enouncement of what
has been observed is, as stated in the paragraph,
called a ivitnessing, — a hearing ivitness, — a testimo7iy,
ko,., these terms being employed in their wider accep-
tation ; and he by whom this declaration is made,
and on whose veracity it rests, is called a ivitness,
voucher, or testijier (testis)!'"' The term testimony, I
may notice, is sometimes, by an abusive metonym,
employed for untness ; and the word evidence is often
ambiguously used for testimony, and for the bearer of
testimony, — the ivitness.
" Such an enouncement, — such a testimony, is, how- The proper
ever, necessary for others, only when the experience Tistlmony.
which it communicates is beyond the compass of their
own observation. Hence it follows, that matters of
reasoning are not proper objects of testimony, since
matters of reasoning, as such, neither can rest nor
ought to rest on the observations of others ; for a
proof of their certainty is equally competent to all,
and may by all be obtained in the manner in which it
was originally obtained by those who may bear wit-
ness to their truth. And hence it further follows, that
matters of experience alone are proper objects of tes-
timony ; and of matters of experience themselves, such
only as are beyond the sphere of our personal expe-
rience. Testimony, in the strictest sense of the term,
therefore, is the communication of an experience, or,
a Esser, Lofjil; § 1 53. — Ed.
VOL. IL M
178
LECTURES ON LOGIC.
LECT.
XXXIII.
Tlie Fact.
Eye-wit-
ness.
Ear-wit-
ness.
what amounts to the same thing, the report of an
observed phsenomenon, made to those whose own
experience or observation has not reached so far.
"The object of testimony, as stated in the para-
graph, is called the fact ; the validity of a testimony
Historical is Called historical credihility. The testimony is either
credibility. . . . '^ . "^ .
immediate or mediate. Immediate, when the witness
has himself observed the fact to which he testifies ;
mediate, when the witness has not himself had experi-
ence of this fact, but has received it on the testimony
of others. The former, the immediate witness, is
commonly styled an eye-witness {testis oculatus) ; and
the latter, the mediate witness, an ear-ivitness [testis
auritus). The superiority of immediate to mediate
testimony is expressed by Plautus, ' Pluris est oculatus
testis unus, quam auriti decem.'" These denominations,
eye and ear witness, are, however, as synoyms of im-
mediate and mediate witness, not always either appli-
cable or correct. The person on whose testimony a
fact is mediately reported, is called the guarantee, or
he on whose authority it rests ; and the guarantee
himself may be again either an immediate or a medi-
ate witness. In the latter case he is called a second-
hand or intermediate ivitness ; and his testimony is
commonly styled hearsay evidence. Further, Testi-
mony, whether immediate or mediate, is either partial
or complete ; either consistent or contradictory. These
distinctions require no comment. Finally, testimony
is either direct or indii^ect ; direct, when the witness
has no motive but that of making known the fact ;
indirect, when he is actuated to this by other ends."^
The Guar-
antee.
Tcstimouics
— Partial,
Complete,
Consistent,
Contradic-
tory.
a Truculentus, II. vi. 8. Cf. Kru^
Loijlk, § 172. Aum. — FiD.
/3 Esser, Lorjllc, § 153.— Ed.
LECTURES ON LOGIC. 179
The only question in reference to Testimony is that lect.
• . . . XXXTII
which regards its Credibility ; and the question con- H^ — '-
earning the credibility of the witness may be compre- Se 'subjicf :
hended under that touching the Credibility of Testi- buity^o'f"
mony. The order I shall follow in the subsequent i^nJeS.
observations is this, — I shall, in the first place, con- Kiity'i^'''
sider the Credibility of Testimony in general ; and, in i^''iJ™ar^
the second, consider the Credibility of Testimony in its Inl^^e™''
particular forms of Immediate and Mediate. iieSate^
First, then, in regard to the Credibility of Testi-
mony in general ; — When we inquire whether a cer-
tain testimony is, or is not, deserving of credit, there
are two things to be considered : 1°, The Object of
the Testimony, that is, the fact or facts for the truth
of which the Testimony vouches ; and, 2°, The Subject
of the Testimony, that is, the person or persons by
whom the testimony is borne. The question, therefore,
concerning the Credibility of Testimony, thus natu-
rally subdivides itself into two. Of these questions,
the first asks, — What are the conditions of the
credibility of a testimony by reference to what is
testified, that is, in relation to the Object of the testi-
mony ? The second asks, — What are the conditions
of the credibility of a testimony by reference to him
who testifies, that is, in relation to the Subject of the
testimony 1 " Of these in their order.
On the first question. — " In regard to the matter i. credi-
testified, that is, in regard to the object of the testi- Testimony
mony; it is, first of all, a requisite condition, that i°, The
what is reported to be true should be possible, both the"'Testi-
absolutely, or as an object of the Elaborative Faculty, its Absolute
and relatively, or as an object of the Presentative '^'" ' ' ^'
a Cf. Esser, Logik, § 154. — Ed.
180 LECTURES ON LOGIC.
LECT. Faculties, — Perception, External or Internal. A tiling
'- is possible absolutely, or in itself, when it can be con-
strued to thought, that is, when it is not inconsistent
with the logical laws of thinking ; a thing is relatively
possible as an object of Perception, External or Inter-
nal, w^hen it can affect Sense or Self-consciousness,
and, through such affection, determine its apprehen-
sion by one or other of these faculties. A testimony
is, therefore, to be unconditionally rejected, if the fact
which it reports be either in itself impossible, or im-
possible as an object of the Presentative Faculties.
Physical But the impossibility of a thing, as an obiect of these
and Mcta- „ . ■•• "^ . .^ "^ . ^
physical faculties, must be decided either upon physical, or
Impossi- . ,. 1 ' • T • ^^
biiity. upon metaphysical, principles. A thing is physically
impossible as an object of sense, when the existence
itself, or its perception by us, is, by the laws of the
material world, impossible. It is metaphysically im-
possible, when the object itself, or its perception, is pos-
sible neither through a natural, nor through a super-
natural, agency. But, to establish the physical impos-
sibility of a thing, it is not sufficient that its existence
cannot be explained by the ordinary laws of nature,
or even that its existence should appear repugnant
with these laws ; it is requisite that an universal and
immutable law of nature should have been demon-
strated to exist, and that this law would be subverted
if the fact in question were admitted to be physically
possible. In like manner, to constitute the metaphy-
sical impossibility of a thing, it is by no means enough
to show that it is not explicable on natural laws, or even
that any natural law stands opposed to it ; it is further
requisite to prove that the intervention even of super-
natural agency is incompetent to its production, that
LECTUEES ON LOGIC. 181
its existence would involve the violation of some neces- lect.
. . , „ XXXIII.
sary principle oi reason.
To establish the credibility of a testimony, in so Relative
r ■... „. -,. Possibility
lar as tins is regulated by the nature oi its object, of an object,
there is, besides the proof of the absolute possibility
of this object, required also a proof of its relative
possibility ; that is, there must not only be no contra-
diction between its necessary attributes, — the attri-
butes by which it must be thought, — but no contra-
diction between the attributes actually assigned to it
by the testimony. A testimony, therefore, which, qua
testimony, is self-contradictory, can lay no claim to
credibility ; for what is self-contradictory is logically
suicidal. And here the only question is, — Does the
testimony, qua testimony, contradict itself "? for if the
repugnancy arise from an opinion of the witness, apart
from which the testimony as such would still stand
undisproved, in that case the testimony is not at once
to be repudiated as false. For example, it would be
wrong to reject a testimony to the existence of a
thing, because the witness had to his evidence of its
observed reality annexed some conjecture in regard to
its orioin or cause. For the latter mio-ht well be
shown to be absurd, and yet the former would re-
main unshaken. It is, therefore, always to be ob-
served, — that it is only the self-contradiction of a
testimony, qua testimony, that is, the self-contradic-
tion of the fact itself, which is peremptorily and irre-
vocably subversive of its credibility.
" We now proceed to the second question ; that is, 2°, The
to consider in general the Credibility of a Testimony tuV'Testi'-
by reference to its Subject, that is, in relation to the jreisona7
Personal Trustworthiness of the Witness. The trust- wcrthincss
182 LECTURES ON LOGIC.
LECT. worthiness of a witness consists of two elements or
' conditions. In the first place, he must be willing, in
wuness ^^^ sccoucl placc, hc must be able, to report the truth.
Sts oTtwo "^^^ ^^'^^ ^^ these elements is the Honesty, — the Sin-
a "^HTnest" verity, — thc Veracity ; the second is the Competency
or Veracity, q£ ^j^g wltucss. Both are cqually necessary, and if
one or other be deficient, the testimony becomes alto-
gether null. These constituents, likewise, do not infer
each other ; for it frequently happens that where the
honesty is greatest the competency is least, and where
the competency is greatest the honesty is least. But
when the veracity of a witness is established, there is
established also a presumption of his competency ; for
an honest man will not bear evidence to a point in re-
gard to which his recollection is not precise, or to the
observation of which he had not accorded the re-
quisite attention. In truth, when a fact depends
on the testimony of a single witness, the competency
of that witness is solely guaranteed by his honesty.
In regard to the honesty of a witness, — this, though
often admitting of the highest probability, never ad-
mits of absolute certainty ; for, though, in many cases,
we may know enough of the general character of the
witness to rely with perfect confidence on his veracity,
in no case can we look into the heart, and observe
the influence which motives have actually had upon
his volitions. We are, however, compelled, in many
of the most important concerns of our existence, to
depend on the testimony, and, consequently, to confide
in the sincerity, of others. But from the moral con-
stitution of human nature, we are warranted in pre-
suming on the honesty of a witness ; and this pre-
sumption is enhanced in proportion as the following
circumstances concur in its confirmation. In the
LECTURES ON LOGIC. ]83
first place, a witness is to be presumed veracious in lect.
this case, in proportion as his love of truth is already ^ ' ^
established from others. In the second place, a wit- Ju^p^tion of
ness is to be presumed veracious, in proportion as he ora^vit-'^
has fewer and weaker motives to falsify his testimony, hanced by
In the third place, a witness is to be presumed vera- IZl^ZnZl.
cious, in proportion to the likelihood of contradiction
which his testimony would encounter, if he deviated
from the truth. So much for the Sincerity, Honesty,
or Veracity of a witness.
" In regard to the Competency or Ability of a wit- 1. compa.
ness, — this, in general, depends on the supposition, that witness.
he has had it in his power correctly to observe the
fact to which he testifies, and correctly to report it.
The presumption in favour of the competence of acircum-
witness rises, in proportion as the following conditions which the
are fulfilled : — In the fir&t place, lie must be presumed uonTcom-
competent in reference to the case in hand, in propor- enhanced!
tion as his general ability to observe and to commu-
nicate his observation has been established in other
cases. In the second place, the competency of a wit-
ness must be presumed, in proportion as in the par-
ticular case a lower and commoner amount of ability
is requisite rightly to observe, and rightly to report
the observation. In the third place, the competency
of a witness is to be presumed, in proportion as it is
not to be presumed that his observation was made or
communicated at a time when he was unable correctly
to make or correctly to communicate it. So much
for the Competency of a witness.
"Now, when both the 2;ood will and the ability, The credi-
' "-" bility 01
that is, when both the Veracity and Competence, ot a Testimony
witness have been sufficiently established, the credi- dated he-
. - . cause the
bility of his testimony is not to be invalidated be-facttesti-
184
LECTURES ON LOGIC.
LECT.
XXXIII.
fied is one
out of the
ordinary
course of
experience.
Summary
regarding
the Credi-
bility of
Testimony
in general.
cause the fact wliicli it goes to prove is one out of tlie
ordinary course of experience."' "^ Thus it woukl be
false to assert, with Hume, that miracles, that is, sus-
pensions of the ordinary laws of nature, are incap-
able of proof, because contradicted by what we have
been able to observe. " On the contrary, where the
trustworthiness of a witness or witnesses is unim-
peachable, the very circumstance that the object is
one in itself unusual and marvellous, adds greater
weight to the testimony ; for this very circumstance
would itself induce men of veracity and intelligence
to accord a more attentive scrutiny to the fact, and
secure from them a more accurate report of their ob-
servation.
" The result of what has now been stated in regard
to the credibility of Testimony in general, is : — That
a testimony is entitled to credit, when the requisite
conditions, both on the part of the object and on the
part of the subject, have been fulfilled. On the part
of the object these are fulfilled, when the object is
absolutely possible, as an ol)ject of the higher faculty
of experience, — the Understanding, — the Elaborative
Faculty, and relatively possible, as an object of the
low^er or subsidiary faculties of experience, — Sense, and
Self-consciousness. In this case, the testimony, qua
testimony, does not contradict itself. On the part of
the subject, the requisite conditions are fulfilled, when
the trustworthiness, that is, the veracity and compe-
tency of the witness, is beyond reasonable doubt. In
regard to the veracity of the witness, — this cannot be
reasonably doubted, when there is no positive ground
on which to discredit the sincerity of the witness, and
when the only ground of doubt lies in the mere gen-
a Esser, Lorjil-, § 154. — Ed.
LECTURES ON LOGIC. 185
eral possibility of deception. And in reference to tlie lect.
. , . xxxin.
competency of a witness, — this is exposed to no rea- -— -
sonable objection, when the ability of the witness to
observe and to communicate the fact in testimony can-
not be disallowed. Having, therefore, concluded the
consideration of testimony in general, we proceed to
treat of it in special, that is, in so far as it is viewed
either as Immediate or as Mediate." " Of these in their
order.
The special consideration of Testimony, w^hen that n. Testi-
testimony is Immediate. — "An immediate testimony, special,, as
... ,T IT- • i'iif> Immediate
or testimony at nrst hand, is one m which the lact and Medi-
reported is an object of the proper or personal expe- 1°, imme-
rience of the reporter. Now it is manifest, that an mony.
immediate witness is in general better entitled to cre-
dit than a witness at second hand ; and his testimony
rises in probability, in proportion as the requisites,
already specified, both on the part of its object and on
the part of its subject, are fulfilled. An immediate
testimony is, therefore, entitled to credit, — 1°, In pro-
portion to the greater ability with wdiich the observ- Conditions
ation has been made ; 2°, In proportion to the less biiity.
impediment in the way of the observation being per-
fectly accomplished ; 3°, In proportion as w^hat was
observed could be fully and accurately remembered ;
and, 4°, In proportion as the facts observed and re-
membered have been communicated by intelligible
and unambifruous sio;ns.
" Now% whether all these conditions of a higher whether
clll tfiCSG
credibility be fulfilled in the case of any immediate conditions
testimony, — this cannot be directly and at once as- in the case
certained ; it can only be inferred, with greater or mediate
less certainty, from the qualities of the witness ; and, cannotX'
directly
a Esser, Lorjik, § 154. — Ed. ascertained.
186 LECTUFxES ON LOGIC.
LECT. consequently, tlie validity of a testimony can only be
'. accurately estimated from a critical knowledge of the
personal character of the witness, as given in his in-
tellectual and moral qualities, and in the circum-
stances of his life, which have concurred to modify
and determine these. The veracity of a witness either
is, or is not, exempt from doubt ; and, in the latter case,
it may not only lie open to doubt, but even be ex-
posed to suspicion. If the sincerity of the witness be
indubitable, a direct testimony is always preferable to
an indirect ; for a direct testimony being made with
the sole intent of establishing the certainty of the fact
in question, the competency of the witness is less ex-
posed to objection. If, on the contrary, the sincerity
of the witness be not beyond a doubt, and, still more,
if it be actually suspected, in that case an indirect
testimony is of higher cogency than a direct ; for
the indirect testimony being given with another view
than merely to establish the fact in question, the in-
tention of the witness to falsify the truth of the fact
has not so strong a presumption in its fiivour. If both
the sincerity and the competency of the witness are
altogether indubitable, it is then of no importance
whether the truth of the fact l)e vouched for by a
single witness, or by a plurality of witnesses. On the
other hand, if the sincerity and competency of the
witness be at all doubtful, the credibility of a testi-
mony will be greater, the greater the number of the
When testi- witucsscs by w^hom the fact is corroborated. But here
tains the it is to bc cousidcred, that when there are a plurality
highest „ . . •■ n 1 • •
degree of 01 tcstimouies to tlic samc tact, these testimonies are
either consistent or inconsistent. If the testimonies
be consistent, and the sincerity and competency of all
the witnesses complete, in that case the testimony
probahitity.
LECTURES ON LOGIC. 187
attains the liighest degree of probability of wliicli any lect.
testimony is capable. Again, if the witnesses be in- ^ ^
Negative
Discre-
pancy.
consistent, — on this hypothesis two cases are pos- ^^^p,
sible ; for either their discrepancy is negative, or it
is positive. A negative discrepancy arises, w^here one
witness passes over in silence what another witness
positively avers. A positive discrepancy arises, where
one witness explicitly affirms something, wdiich some-
thing another witness explicitly denies. When the
difference of testimonies is merely negative, we may
suppose various causes of the silence ; and, therefore,
the positive averment of one witness to a fact is not
disproved by the mere circumstance, that the same
fact is omitted by another. But if it be made out,
that the witness who omits mention of the fact, could
not have been ignorant of that fact had it taken place,
and, at the same time, that he could not have passed
it over without violating every probability of human
action, — in this case, the silence of the one witness
manifestly derogates from the credibility of the other
witness, and in certain circumstances may annihilate
it altogether. Where, again, the diflference is positive,
the discrepancy is of greater importance, because,
(though there are certainly exceptions to the rule),
an overt contradiction is, in general and in itself, of
stronger cogency than a mere non-confirmation by
simple silence. Now the positive discrepancy of tes-
timonies either admits of conciliation, or it does not.
In the former case, the credibility of the several testi-
monies stands intact ; and the discrepancy among the
witnesses is to be accounted for by such circumstances
as explain, without invalidating, the testimony con-
sidered in itself. In the latter case, one testimony
manifestly detracts from the credibility of another ;
188 LECTURES ON LOGIC.
LF.cT. for of incompatible testimonies, while botli cannot be
XXXIII
— ^ — '- true, the one must be false, when reciprocally contra-
dictory, or they may both be false, when reciprocally
contrary. In this case, the whole question resolves
itself into one of the greater or less trustworthiness of
the opposing witnesses. Is the trustworthiness of the
counter-witnesses equally great ■? In that case, neither
of the conflictive testimonies is to be admitted. Again,
is the trustworthiness of the witnesses not upon a par'?
In that case, the testimony of the witness whose trust-
worthiness is the greater, obtains the preference, — and
this more especially if the credibility of the other wit-
nesses is suspected." "'
So much for the Credibility of Testimon)^, considered
in Sjiecial, in so far as that testimony is Immediate or
at First Hand ; and I now, in the second place, pass on
to consider, likewise in special, the Credibility of Testi-
mony, in so far as that testimony is Mediate, or at
Second Hand.
2°, Mediate " A Mediate Testimony is one where the fact is an
Testiraouv. ,. n t\ it c t^ • -r-\
object not oi rersonal, but oi loreign Jiixperience.
Touching the credibility of a mediate testimony, this
supposes that the report of the immediate, and that
the report of the mediate, witness are both trust-
worthy. Whether the report of the immediate w^itness
be trustworthy, — this we are either of ourselves able to
determine, viz., from our personal acquaintance with
his veracity and competence ; or we are unable of
ourselves to do this, in which case the credibility of
the immediate must be taken upon the authority of
the mediate witness. Here, however, it is necessary
for us to be aware, that the mediate witness is pos-
a Esser, Lor/ik, § 155. — Ed.
LECTURES ON LOGIC. 189
sessed of the ability requisite to estimate the credi- lect.
bility of the immediate witness, and of the honesty to 1— ^ — '.
communicate the truth without retrenchment or falsi-
fication. Bnt if the trustworthiness both of the
mediate and of the immediate witness be sufficiently
established, it is of no consequence, in regard to the
credibility of a testimony, whether it be at first hand
or at second. Nay, the testimony of a mediate may
even tend to confirm the testimony of an immediate
witness, when his own competence fairly to appreciate
the report of the immediate witness is indubitable.
If, however, the credibility of the immediate witness be
unimpeachable, but not so the credibility of the medi-
ate, in that case the mediate testimony, in respect of its
authority, is inferior to the immediate, and this in the
same proportion as the credibility of the second hand
witness is inferior to that of the witness at first hand.
Further, mediate witnesses are either Proximate or Mediate
Eemote ; and, in both cases, either Independent or De- are either
pendent. The trustworthiness of proximate witnesses or™Remote,
is, in general, greater than the trustworthiness of re- indepen-
mote ; and the credibility of independent witnesses Dependent,
greater than the credibility of dependent. The re-
mote witness is unworthy of belief, when the inter-
mediate links are w^anting between him and the
original witness ; and the dependent witness deserves
no credit, when that on which his evidence depends
is recognised as false or unestablished. Mediate tes-
timonies are, likewise, either direct or indirect ; and,
likewise, when more than one, either reciprocally con-
gruent or conflictive. In both cases the credibility of
the witnesses is to be determined in the same manner
as if the testimonies were immediate.
lijO LECTUEES ON LOGIC.
LECT. " The testimony of a plurality of mediate witnesses,
XXXIII •/ 1- 'j^
'- where there is no recognised immediate witness, is
Shat"''" called a rumour, if the witnesses be contemporaneous;
Traditiou. ^^^ ,^ iraditiou, if the witnesses be chronologically suc-
cessive. These are both less entitled to credit, in pro-
portion as in either case a fiction or falsification of the
fact is comparatively easy, and, consequently, com-
paratively probable." '*
a Easer, Loyilc, § 156. — Ed,
LECTURES ON LOGIC. J 91
LECTURE XXXIV.
MODIFIED METHODOLOGY.
SECTION I. — OF THE ACQUISITION OF KNOWLEDGE.
I. EXPERIENCE. — B. FOREIGN : — RECORDED TESTIMONY
AND WRITINGS IN GENERAL.
II. SPECULATION.
In our last Lecture, we were engaged in the considera- ^^iv
tion of Testimony, and the Principles by which its Cre-
,.,.,.. , -, .. , , Criticism of
dibility IS governed, — on the supposition always that Recorded
1 -Ti o ^ • 1 Testimony,
we possess the veritable report oi the witness whose and of
. . f. -^ . . Writings
testimony it proiesses to be ; and on the supposition in general.
that we are at no loss to understand its meaning and
purport. But questions may arise in regard to these
points, and, therefore, there is a further critical process
requisite, in order to establish the Authenticity, — the
Integrity, and the Signification, of the documents in
which the testimony is conveyed. This leads us to the
important subject, — the Criticism of Recorded Testi-
mony, and of Writings in general. I shall comprise the
heads of the following observations on this subject in
the ensuing paragraph.
H ex. The examination and judgment ofpar. ex.
Writings professing to contain the testimony of andTuter-
certain witnesses, and of Writings in General pro- p^*^*^^''""'
192 LECTURES ON LOGIC.
LECT. fessing to be the work of certain authors, is of
1 two parts. For the inquiry regards either, 1°,
The Authenticity of the document, that is,
whether it be, in whole or in part, the product of
its ostensible author ; for ancient writings in
particular are frequently supposititious or inter-
polated ; or 2°, It regards the Meaning of the
words of which it is composed, for these, espe-
cially when in languages now dead, are frequently
obscure. The former of these problems is re-
solved by the ^r^ of Criticism, (Critica), in the
stricter sense of the term ; the latter by the Art
of Interpretation, [Exegetica or Hermeneutica) .
Criticism is of two kinds. If it be occupied with
the criteria of the authenticity of a writing in its
totality, or in its principal parts, it is called the
Higher, and sometimes the Internal, Criticism.
If, again, it consider only the integrity of particu-
lar words and phrases, it is called the Lower, and
sometimes the External, Criticism. The former
of these may perhaps be best styled the Criticism
of Authenticity ; — the latter, the Criticism of In-
tegrity.
The problem which Interpretation has to solve
is, — To discover and expound the meaning of a
writer, from the words in which his thou2;hts are
expressed. It departs from the principle, that
however manifold be the possible meanings of
the expressions, the sense of the writer is one.
Interpretation, by reference to its sources or sub-
sidia, has been divided into the Grammatical, the
Histo^ncal, and the Philosophical, Exegesis."'
a Cf. Krug Loyik, § 177 fi scq. — Kiesewetter, Lvjll; ]i. ii. § 185 ct seq.]
Ed. [Snell, Logik, p. ii. § 6 p. 195.
LECTURES ON LOGIC. 193
"Testimonies, especially when the ostensible wit- lect.
nesses themselves can no longer be interrogated, may
be snbjected to an examination under various forms ; ^^^^"'*'
and this examination is in fact indispensable, seeing
not only that a false testimony may be substituted for
a true, and a testimony true upon the whole may yet be
falsified in its parts, — a practice which prevailed to a
great extent in ancient times ; while at the same time
the meaning of the testimony, by reason either of the
foreign character of the language in which it is ex-
pressed, or of the foreign character of thought in which
it is conceived, may be obscure and undetermined.
The examination of a testimony is twofold, inasmuch The exa-
. , . . n ' K ^ • • 1 niination of
as it IS either an examination oi its Authenticity and a testimony
T • • • o • HIT • rm • '■wofold, —
Integrity, or an examination oi its Meaning. ihisofitsAu-
PTT f, ... Til • thenticity
twoiold process oi examination is applicable to testi- and integ-
monies of every kind, but it becomes indispensable itsMeaning.
when the testimony has been recorded in writing, and
when this, from its antiquity, has come down to us
only in transcripts, indefinitely removed from the ori-
ginal, and when the witnesses are men differing
greatly from ourselves in language, manners, customs
and associations of thought. The solution of the Criticism,
problem, — By what laws are the authenticity or
spuriousness, the integrity or corruption, of a writing
to be determined, — constitutes the Art of Criticism, in
its stricter signification {Critica) ; and the solution of interpreta-
the problem, — By what law is the sense or meaning
of writing to be determined, — constitutes the Art of In-
terpretation or Exposition {Hermeneutica, Exegetica).
In theory. Criticism ought to precede Interpretation,
for the question, — Who has spoken, naturally arises
before the question, — How what has been spoken is to
be understood. But in practice, criticism and inter-
VOL. IL N
194) LECTURES ON LOGIC.
LECT. pretation cannot be separated ; for in application they
'- proceed hand in hand." "
I. Criticism. "First, then, of Criticism, and the question that pre-
sents itself in the threshold is, — What are its Defini-
tion and Divisions ? Under Criticism is to be under-
stood the complement of logical rules, by which the
authenticity or spuriousness, the integrity or interpo-
lation, of a writing is to be judged. The problems
itsprob- which it proposes to answer are — 1°, Does a writing
really proceed from the author to whom it is ascribed ;
and, 2°, Is a writing, as we possess it, in all its parts
the same as it came from the hands of its author.
The system of fundamental rules, which are supposed
in judging of the authenticity and integrity of every
writing, constitutes what is called the Doctinne of
Universal U7iiversal Criticism ; and the system of particular
rules, by which the authenticity and integrity of
writings of a certain kind are judged, constitutes the
Special doctrine of what is called Special Criticism. It is
manifest, from the nature of Logic, that the doctrine i
Universal of Uuivcrsal Criticism is alone within its sphere. Now
aionrwi'thin Uuivcrsal Criticism is conversant either with the
of L^gi^^ authenticity or spuriousness of a writing considered
as a whole, or with the integrity or interpolation of
Its Divi- certain parts. In the former case it is called Higher, !
in the latter Lower, Criticism ; but these denomina-
tions are inappropriate. The one criticism has also
been styled the Internal, the other the External ; but
these appellations are, likewise, exceptionable ; and,
perhaps, it would be preferable to call the former the ;
Criticism of the Anthe7\ticity, the latter, the Criticism i
of the Integrity, of a work. I shall consider these in
particular, and, first, of the Criticism of Authenticity.
a Esser, Logik, § 157 Ed.
sions
LECTURES ON LOGIC. 195
"A proof of the authenticity of a writino;, more lect.
XXXIV
especially of an ancient writing, can be rested only
upon two grounds, — an Internal and an External, — ofAuthen^
and on these either apart or in combination. By in- *'"*^'
ternal grounds, we mean those indications of authen-
ticity which the writing itself affords. By external
grounds, we denote the testimony borne by other
works of a corresponding antiquity, to the authen-
ticity of the writing in question.
" In reo;ard to the Internal Grounds ; — it is evident, a. internal
^ _ _ Grounds.
without enterins; upon details, that these cannot of These of
^, themselves
themselves, that is, apart from the external grounds, not sutE-
afford evidence capable of establishino; beyond a doubt establish
, -, . . f. . . ? „ the authen-
the authenticity oi an ancient writing ; lor we can ticity of a
easily conceive that an able and learned forger may
accommodate his fabrications both to all the general
circumstances of time, place, people, and language,
under which it is supposed to have been written, and
even to all the particular circumstances of the style,
habit of thought, personal relations, &c. of the author
by whom it professes to have been written, so that
everything may militate for, and nothing militate
against, its authenticity.
" But if our criticism from the internal grounds But onmi-
alone be, on the one hand, impotent to establish, it is, disprove"
on the other, omnipotent to disprove. For it is suffi-
cient to show that a writing is in essential parts, that
is, parts which cannot be separated from the whole,
in opposition to the known manners, institutions,
usages, &c., of that people with which it would, and
must, have been in harmony, were it the product of
the writer whose name it bears ; that, on the contrary,
it bears upon its face indications of another country
or of a later age ; and, finally, that it is at variance
196 LECTURES ON LOGIC.
LECT. with, the personal circumstances, the turn of mind,
XXXIV
— '- and the pitch of intellect, of its pretended author.
And here it is to be noticed, that these grounds are
only relatively internal ; for we become aware of
them originally only through the testimony of others,
that is, through external grounds." '^
b. External In regard to the External Grounds : — they, as I
Grounds. ^ . . , . , . . , . "^ .
said, consist m the testimony, direct or indirect, given
to the authenticity of the writing in question by other
works of a competent antiquity. This testimony may
be contained either in other and admitted writino;s of
the supposed author himself ; or in those of contem-
porary writers ; or in those of writers approximat-
ing in antiquity. This testimony may also be given
either directly, by attribution of the disputed writing
by title to the author ; or indirectly, by quoting as
his, certain passages which are to be found in it. On
this subject it is needless to go into detail, and it is
hardly necessary to observe, that the proof of the
authenticity is most complete when it proceeds upon
the internal and external grounds together. I, there-
fore, pass on to the Criticism of Integrity. ^
2. Criticism " Wlicu thc authenticity of an ancient work has
been established on external grounds, and been con-
firmed on internal, the Integrity of this writing is
not therewith proved ; for it is very possible, and in
ancient writings indeed very probable, that particular
passages are either interpolated or corrupted. The
authenticity of particular passages is to be judged of
precisely by the same laws, which regulate our criti-
cism of the authenticity of the whole work. The proof
most pertinent to the authenticity of particular pas-
o Esser, Logik, § 158-160.— Ed. /3 See Esser, Logik, §§ 161, 162.— Ed.
LECTURES ON LOGIC. 197
sao^es is drawn — 1° From tlieir ackDOwledsment by lect.
. a J XXXIV
the author himself in other, and these unsuspected, 1
works ; 2°, From the attribution of them to the author
by other writers of competent information ; and, 3°,
From the evidence of the most ancient MSS. On the
other hand, a passage is to be obelized as spurious, —
1°, When found to be repugnant to the general relations
of time and place, and to the j^ersonal relations of the
author ; 2°, When wanting in the more ancient codices,
and extant only in the more modern. A passage is
suspicious, when any motive for its interpolation is
manifest, even should we be unable to establish it as
spurious. The differences which different copies of a
writing exhibit in the particular passages, are called
various readings (varice lectiones or lectiones vari-
antes). Now, as of various readings one only can be
the true, while they may all very easily be false, the
problem which the criticism of Integrity proposes to
solve is,— How is the genuine reading to be made out,
— and herein consists what is technically called the
Recension, more properly the Emendation, of the text.
"The Emendation of an ancient author may be of Emendation
• of tilG text
two kinds ; the one of which may be called the His- -of two
torical, the other the Gonjectwxd. The former of these Historical'
founds upon historical data for its proof ; the latter, jecturai.
again, proceeds on grounds which lie beyond the sphere
of historical fact, and this for the very reason that his-
torical fact is found incompetent to the restoration of
the text to its original integrity. The historical emen-
dation necessarily precedes the conjectural, because the
object itself of emendation is wholly of an historical
character, and because it is not permitted to attempt
any other than an emendation on historical grounds,
198 LECTUKES ON LOGIC.
LECT. until, from these very 2;rounds themselves, it be shown
XXXIV .
1 that the restitution of the text to its original integrity
Historical cauuot be historically accomplished. Historical Emen-
kb^ds— ^^tion is again of two kinds, according as its judgment
External procccds ou extcmal or on internal ^'rounds. It founds
and Inter- ^ o
^'^i- upon external grounds, when the reasons for the truth
or falsehood of a reading are derived from testimony ;
it founds upon internal grounds, wdien the reasons for
the truth or falsehood of a reading are derived from
the writing itself. Historical emendation has thus a
twofold function to perform, (and in its application to
practice, these must always be performed in conjunc-
tion), viz., it has carefully to seek out and accurately
to weigh both the external and internal reasons in sup-
port of the reading in dispute. Of external grounds
the princijjal consists in the confirmation afforded by
MSS., by printed editions which have immediately
emanated from MSS., by ancient translations, and by
passages quoted in ancient authors. The internal
grounds are all derived either from the form, or from
the contents, of the work itself. In reference to the
form, — a reading is probable, in proportion as it cor-
responds to the general character of the language pre-
valent at the epoch when the work was written, and
to the peculiar character of the language by which the
author himself was distinguished. In reference to the
contents, — a reading is probable, when it harmonises
with the context, that is, when it concurs with the
other words of the particular passage in which it
stands, in affording a meaning reasonable in itself, and
conformable with the author's opinions, reasonings,
and general character of thought.'"'
a Esaer, Loijlk, § 163.— Ed.
LECTURES ON LOGIC. 199
It frequently happens, however, that, notwithstand- lect.
ing the uniformity of MSS. and other external sub- — ^ — 1
sidia, a reading cannot be recognised as genuine. In imemia-'^'^'
this case, it must be scientifically shown from the ^'°'^'
rules of criticism itself, that this lection is corrupt.
If the demonstration thus attempted be satisfactory,
and if all external subsidia have been tried in vain,
the critic is permitted to consider in what manner the
corrupted passage can be restored to its integrity.
And here the conjectural or divinatory emendation
comes into play ; a process in which the power and
eflficiency of criticism and the genius of the critic are
principally manifested," "
So much for Criticism, in its applications both to
the Authenticity and to the Integrity of Writings.
We have now to consider the general rules by which
Interpretation, that is, the scientific process of ex-
pounding the Meaning of an author, is regulated.
" By the Art of Interpretation, called likewise techni- it. inter-
cally Hei^meneutic or Exegetic, is meant the comple-
ment of logical laws, by which the sense of an ancient
writing is to be evolved. Hermeneutic is either Gen- General and
Special.
eral or Special. General, when it contains those laws
which apply to the interpretation of any writing
whatever ; Special, when it comprises those laws by
which writings of a particular kind are to be ex-
pounded. The former of these alone is of logical
concernment. The problem proposed for the Art of
Interpretation to solve, is, — How are we to proceed
in order to discover from the words of a writing that
sole meaning which the author intended them to
convey \ In the interpretation of a work, it is not,
a Esser, Log tic, § 166. — Ed. [Par- Geiiuensis, Ars Logico-Critica, L. iv.
rhasiana, i. 359-365, 2d ed. 1701. c. vi. ct seq.]
200 LECTURES ON LOGIC.
LECT. therefore, enough to show in what signification its
XXXIV ...
'- words may be understood ; for it is required that we
show in what signification they must. To the execu-
tion of this task two conditions are absolutely neces-
sary ; 1°, That the interpreter should be thoroughly
acquainted with the language itself in general, and
with the language of the writer in particular ; and 2°,
That the interpreter should be familiar with the sub-
jects of which the writing treats. But these two
requisites, though indispensable, are not of themselves
sufiicient. It is also of importance that the expo-
sitor should have a competent acquaintance with the
author's personal circumstances and character of
thought, and with the history and spirit of the age
and country in which he lived. In regard to the inter-
pretation itself ; — it is to be again observed, that as a
writer could employ expressions only in a single sense,
so the result of the exposition ought to be not merely
to show what meaning may possibly attach to the
doubtful terms, but what meaning necessarily must.
When, therefore, it appears that a passage is of doubt-
ful import, the best preparative for a final determin-
ation of its meaning is, in the first place, to ascertain
in how many different significations it may be con-
strued, and then, by a process of exclusion, to arrive
at the one veritable meaning. When, however, the
obscurity cannot be removed, in that case it is the
duty of the exjDositor, before abandoning his task, to
evince that an interpretation of the passage is, with-
out change, absolutely or relatively impossible.
Sources of " As to the sourccs from whence the Interpretation
^nwprea ^^ ^^ ^^ drawu, — tlicsc are three in aU, — viz., 1°, The
Tractus literarum, the words themselves, as they ap-
pear in MSS. ; 2°, The context, that is, the passage
LECTURES ON LOGIC. 201
in immediate connection with the doubtful term ; 3°, lect.
Parallel or analogous passages in the same, or in other, '~
writings." " How the interpretation drawn from these
sources is to be applied, I shall not attempt to detail ;
but pass on to a more generally useful and interesting
subject.
So much for Experience or Observation, the first Specuiatiou
mean of scientific discovery, that, viz., by which we Means of
1 -, I . , . , Knowledge.
apprehend what is presented as contingent phseno-
mena, and by whose processes of Induction and
Analogy we carry up individual into general facts.
We have now to consider the other Mean of scientific
discovery, that, viz, by which, from the phsenomena
presented as contingent, we separate what is really
necessary, and thus attain to the knowledge, not of
merely generalised facts, but of universal laws. This
mean may, for distinction's sake, be called Specula-
tion, and its general nature I comprehend in the fol-
lowing paragraph.
IF CXI. When the mind does not rest con- Par. cxi.
tented with observing and classifying the objects —as a
(, . . ■, 1 n • 1 • nieans of
01 its experience, but, by a reilective analysis. Knowledge.
sunders the concrete wholes presented to its
cognition, throws out of account all that, as con-
tingent, it can think away from, and concen-
trates its attention exclusively on those elements
which, as necessary conditions of its own acts, it
cannot but think : — by this process it obtains the
knowledge of a certain order of facts, — facts of
Self-consciousness, which, as essential to all Ex-
perience, are not the result of any ; constituting
o Eeser, LogiJc, § 167.— Ed. [Cf. Snell, Loyil-, p. ii. § 6, p. 200.]
202 LECTURES ON LOGIC.
LECT. ill truth tlie Laws by which the possibility of our
^^^^^- cognitive functions is determined. This process,
by which we thus attain to a discriminative
knowledge of the Necessary, Native, and, as they
are also called, the Noetic, Pure, a ijriori, or
Transcendental, Elements of Thought, may be
styled Speculative Analysis, Analytic Specula-
tion, or Speculation simply, and is carefully to be
distinguished from Induction, with which it is
not unusually confounded.
tion
Expiica- " The empirical knowledge of which we have
hitherto been speaking, does not, however varied and
extensive it may be, suffice to satisfy the thinking
mind as such ; for our empirical knowledge itself
points at certain higher cognitions from which it may
obtain completion, and which are of a very different
character from that by which the mere empirical cog-
nitions themselves are distinguished. The co2;nitions
are styled, among other names, by those of noetic,
pure, or rational, and they are such as cannot, though
manifested in experience, be derived from experience ;
for, as the conditions under which experience is pos-
sible, they must be viewed as necessary constituents
of the nature of the thinking principle itself. Philo-
sopbers have indeed been found to deny the reality of
such cognitions native to the mind ; and to confine
the whole sphere of human knowledge to the limits of
experience. But in this case philosophers have over-
looked the important circumstance, that the acts, that
is, the apprehension and judgment, of experience, are
themselves impossible, except under the supposition of
certain potential cognitions previously existent in the
thinking subject, and which become actual on occa-
LECTURES ON LOGIC. 203
sion of an obiect beina; presented to tlie external or lect.
... xxxiv
internal sense. As an example of a noetic cognition, 1 1
the following propositions may suffice : — An object
and all its attributes are convertible ; — All that is
has its sufficient cause. The principal distinctions of Principal
Empirical and Rational Knowledges, or rather Em-ofEmpiri-
pirical and Noetic Cognitions, are the following : — 1°, Noetic Cog-
Empirical cognitions originate exclusively in experi-°'^*^
ence, whereas noetic cognitions are virtually at least
before or above all experience, — all experience being
only possible through them. 2°, Empirical cognitions
come piecemeal and successively into existence, and
may again gradually fade and disappear ; whereas
noetic cognitions, like Pallas armed and immortal from
the head of Jupiter, spring at once into existence, com-
plete and indestructible. 3°, Empirical cognitions find
only an application to those objects from which they
were originally abstracted, and, according as things ob-
tain a different form, they also may become differently
fashioned ; noetic cognitions, on the contrary, bear
the character impressed on them of necessity, uni-
versality, sameness. Whether a cognition be empirical
or noetic, can only be determined by considering
whether it can or cannot be presented in a sensible
perception ; — whether it do or do not stand forward
clear, distinct, and indestructible, bearing the stamp
of necessity and absolute universality. The noetic
cognitions can be detected only by a critical analysis
of the mental pheenomena proposed for the purpose of
their discovery;"" and this analysis may, as I have
said, be styled Speculation, for want of a more appro-
priate appellation.
a Esser, Logil-, § 171. — Ed.
201
LECTURES ON LOGIC.
LECTURE XXXV.
MODIFIED METHODOLOGY.
SECTION I. — OF THE ACQUISITION OF KNOWLEDGE.
III. COMMUNICATION OF KNOWLEDGE. A. INSTRUCTION
ORAL AND WRITTEN. B. CONFERENCE
DIALOGUE AND DISPUTATION.
LECT. I NOW 0^0 on to the last Mean of Acquiring and Per-
_1^^ fecting our knowledge ; and commence with the fol-
lowing paragraph : —
Par. OXII,
The Cora-
municaliou
of Thought,
— as a
means of
Acquiring
and Per-
fecting
Knowledge.
H CXI I. An important mean for the Acqui-
sition and Perfecting of Knowledge is the Com-
munication of Thought. Considered in general,
the Communication of thought is either One-sided,
or Mutual. The former is called Instruction
{institutio), the latter Conference {collocutio) ;
but these, though in theory distinct, are in prac-
tice easily combined. Instruction is again either
Oral or Written ; and Conference, as it is inter-
locutory and familiar, or controversial and solemn,
may be divided into Dialogue [colloquium, dia-
logus), and Disputation ( disputatio, concertatio)-
The Communication of thought in all its forms
is a means of intellectual improvement, not only
LECTURES ON LOGIC. 205
to him who receives, but to him who bestows, lect.
information ; in both relations, therefore, it ought -
to be considered, and not, as is usually done, in
the latter only."
In illustrating this paragraph, I shall commence Expiica-
with the last sentence, and, before treating in detail
of Instruction and Conference, as means of extendino-
the limits of our knowledge by new acquisitions de-
rived from the communication of others, I shall en- The Com-
deavour to show, that the Communication of thought of™hougiu
is itself an important mean towards the perfecting of unt'^ean
knowledge in the mind of the communicator himself. p°eXcting^
In this view, the communication of knowledge is like LdgeTiTthe
the attribute of mercy, twice blessed, — " blessed to ™mmunicr-
him that gives and to him that takes ;" in teaching
others we in fact teach ourselves.
This view of the reflex effect of the communication
of thought on the mind, whether under the form of
Instruction or of Conference, is one of high importance,
but it is one w^hich has, in modern times, unfortunately
been almost wholly overlooked. To illustrate it in
all its bearings would require a volume, — at present
I can only contribute a few hints towards its expo-
sition.
Man is, by an original tendency of his nature, de- Man natu-
termined to communicate to others what occupies his mined to
communica-
thoughts, and by this communication he obtains ation.
clearer understanding of the subject of his cogitations
than he could otherwise have compassed. This fact This fact
- . , , P -,-., T 1 7^ noticed by
did not escape the acuteness oi rlato. In tne Jrvota- piato.
goras, — " It has been well," says Plato (and he has
a Cf. Knig, Logik, § 181 et seq. — Ed.
20G LECTURES ON LOGIC.
LECT. sundry passages to the point), — " It lias been well, I
think, observed by Homer —
' Through mutual intercourse and mutual aid,
Great deeds are done and great discoveries made ;
The wise new wisdom on the wise bestow,
Whilst the lone thinker's thoughts come slight and slow.' o
For in company we, all of us, are more alert, in deed
and word and thought. And if a man excogitate
aught hy himself, forthwith he goes about to find some
one to whom he may reveal it, and from vAom he may
obtain encouragement, aye and until his discovery be
completed!'^ The same doctrine is maintained by
Aristotle. Aristotlc, and illustrated by the same quotation ; "^
(to which, indeed, is to be referred the adage, — "Unus
Themistius. homo, uullus liomo.") — " We rejoice," says Themistius,
" in hunting truth in company, as in hunting game." ^
Luciiius. Lucilius, — " Scire est nescire, nisi id me scire alius
scierit ; ^ — paraphrased in the compacter, though far
Persius. inferior, verse of Persius, — " Scire tuum nihil est, nisi
Cicero. tc sciro hoc sciat alter."^ — Cicero's Cato testifies to
the same truth : — " Non facile est invenire, qui quod
Seneca. sciat ipsc, uou tradat alteri." "^ And Seneca : — " Sic
cum hac exceptione detur sapientia, ut illam inclusam
teneam nee enunciem, rejiciam. Nullius boni, sine
socio, jucunda possessio est." ^
" Condita tabescit, vulgata scientia crescit." *
a Altered from Pope's Homer, Book f I. 27. — Ed.
X. 265. 7) Cato apud Cicero, De Fin., iii.
fi Protag., p. 348. Compare Lee- c. 20, § 66.
tures on Metaphysics, i. p. 376. B Seneca, Ep., vi.
7 Eth. Nlc., viii. 1. t Quoted also in Discussions, p. 778.
5 Orat., xxi. Explorator aut Philo- This line appears to have been taken
sopJtus, Orationes, p. 254, ed. Harduin, from a small volume, entitled, Car-
Paris, 1684. — Ed. minum Prorerbialium Loci Communes,
€ Fragm., 25, in the Bipont edition p. 17, Lond. 1583 ; but the author is
of Persius and Juvenal, p. 176. — Ed. not named. — Ed.
LECTURES ON LOGIC. 207
" In hoc gaudeo aliquid discere, ut doceam : nee me lect.
uUa res delectabit, licet eximia sit et salutaris, quam 11 1
mihi uni, sciturus sim." '^ " Ita non solum ad discen-
dum propensi snmus, verum etiam ad docendum,"/^
The modes in which the Communication of thought Modes m
is conducive to the perfecting of thought itself, are munication
_ - . _ . _ . ^ is conducive
two ; lor the mind may be determined to more ex- to the Per-
alted energy by the sympathy of society, and by the Thought
stimulus of opposition ; or it may be necessitated
to more distinct, accurate, and orderly thinking, as
this is the condition of distinct, accurate, and orderly
communication. Of these the former requires the
presence of others during the act of thought, and is,
therefore, only manifested in oral instruction or in
conference ; whereas the latter is operative both in
our oral and in our written communications. Of these
in their order.
In the first place, then, the influence of man on i. By red-
man in reciprocally determining a higher energy oflCTmLing'
the faculties, is a phsenomenon sufiiciently manifest. euerVof
By nature a social being, man has powers which aretiel""^"
relative to, and, consequently, find their development L mpTth^^
in, the company of his fellows ; and this is more par-
ticularly shown in the energies of the cognitive facul-
ties. "As iron sharpeneth iron," says Solomon, "so a
man sharpeneth the understanding of his friend."'^
This, as I have said, is efiected both by fellow-feeling
and by opposition. We see the efiects of fellow-feel-
ing, in the necessity of an audience to call forth the
exertions of the orator. Eloquence requires numbers ;
and oratory has only flourished where the condition
o Seneca, Epist., vi. — Ed. rised vei'sion is, countenance of his
j3 Cicero, De Fin. iii. 20. — Ed. friend. Compare Lectures on Meta-
y Proverbs, xxvii. 17. The autho- physics, vol. i. p. 376. — Ed.
208 LECTURES ON LOGIC,
LECT. of large audiences has been supplied. But opposition
is perhaps still more powerful than mere sympathy in
dpposiUon. calling out the resources of the intellect
Plutarch, In the mental as in the material world, action and
reaction are ever equal ; and Plutarch'^ well ob-
serves, that as motion would cease were contention
to be taken out of the physical universe, so pro-
gress in improvement would cease were contention
taken out of the moral ; vroXe/xos olttolvtcop rraTi/jp.^
Scaiiger, " It is maintained," says the subtle Scaliger, " by
Vives, that we profit more by silent meditation than
by dispute. This is not true. For as fire is elicited
by the collision of stones, so truth is elicited by the
collision of minds, I myself (he adds) frequently
meditate by myself long and intently ; but in vain ;
unless I find an antagonist, there is no hope of a
successful issue. By a master we are more excited
than by a book ; but an antagonist, whether by
his pertinacity or his wisdom, is to me a double
master," '''
2, By im- But, iu tlic sccoud placc, the necessity of communi-
nece^lty of catlug a plccc of kuowledgo to others, imposes upon
obtaining a .i ,, f*ii"* pn • r
fuller con- Hs thc ueccssity 01 obtammg a luller consciousness oi
of'know-^ that knowledge for ourselves. This result is to a cer-
ouileives. taiu extcut secured by the very process of clothing our
cogitations in words. For speech is an analytic pro-
cess ; and to express our thoughts in language, it is
requisite to evolve them from the implicit into the
explicit, from the confused into the distinct, in order
to bestow on each part of the organic totality of a
thought its precise and appropriate symbol. But to
a Vifa Agesilai, Opera, 1599, vol. i. Philos., i. p. 158. — Ed.
p. 598. — Ed, 7 E.vercit., f. 420. [For a criticism
Hei-aclitus. Cf. Plutarch, De Is. of Sealiger's remark as regards Vives,
tt 0$ir., p. 370. Brandis, Gesch. der see Discussions, p. 773. — Ed.]
LECTURES ON LOGIC. 209
do this is in fact only to accomplish the first step lect.
XXXV
towards the perfecting of our cognitions or thoughts. ^
But the communication of thouo;ht, in its hio-her ap- influence of
T • . r 1 1 • 1 • Composi.
plications, imposes on us far more than this ; and m tion and
1 • • • 1 •^^ 1 r> • ^ • n Instruction
SO doing it reacts with a still more beneficial mfiuence inperfecting
11' r» 1 • 1 • n 1 "^^ Know-
on our habits of thinking, buppose that we are not ledge.
merely to express our thoughts as they spontaneously
arise; suppose that we are not merely extemporane-
ously to speak, but deliberately to write, and that
what we are to communicate is not a simple and easy,
but a complex and difficult, matter. In this case, no
man will ever fully understand his subject who has
not studied it with the view of communication, while
the power of communicating a subject is the only
competent criterion of his fully understanding it.
"When a man," says Godwin, "writes a book of method- Godwin
ical investigation, he does not write because he under-
stands the subject, but he understands the subject
because he has written. He was an uninstructed tyro,
exposed to a thousand foolish and miserable mistakes,
when he began his work, compared with the degree
of proficiency to which he has attained when he has
finished it. He who is now an eminent philosopher,
or a sublime poet, was formerly neither the one nor
the other. Many a man has been overtaken by a pre-
mature death, and left nothing behind him but com-
positions worthy of ridicule and contempt, who, if he
had lived, would perhaps have risen to the highest
literary eminence. If we could examine the school
exercises of men who have afterwards done honour to
mankind, we should often find them inferior to those
of their ordinary competitors. If we could dive into
the portfolios of their early youth, we should meet
with abundant matter for laughter at their sense-
VOL. IL
210
LECTURES ON LOGIC.
LECT.
XXXY.
Aristotle.
less iDcongruities, and for contemptuous astonish-
ment.""
" The one exclusive sign," says Aristotle, " that a
man is thoroughly cognisant of anything is that he is
able to teach it;"^ and Ovid, — ^
" Quodque pariun novit nemo clocere potest."
In this reactive effect of the communication of
knowledge in determining the perfection of the know-
ledge communicated, originated the scholastic maxim
Doce lit discas, — a maxim which has unfortunately
been too much overlooked in the schemes of modern
education. In former ages, teach that you may learn,
always constituted one at least of the great means of
intellectual cultivation. "To teach," says Plato, "is
the way for a man to learn most and best."^ "Hom-
ines dum decent discunt," says Seneca.^ " In teach-
ciementof iug," says Clement of Alexandria,^ "the instructor often
' " learns more than his pupils." " Disce sed a doctis ;
Dionysius indoctos ipse doceto," is the precept of Dionysius Cato ;''
and the two following were maxims of authority in
the discipline of the middle ages. The first —
, " Multa rogare, rogata tenere, retenta docere,
Haec tria, discipulum faciunt superare magistrum." &
The second —
" Discere si quaeris doceas ; sic ijise doceris ;
Nam studio tali tibi proficis atque sodali." '
Plato.
Seneca.
a Enquirer, Part i. Essay iv. pp.
23, 24, ed. 1797.— Ed.
/3 Metajjhys., i. L Quoted in Z);s-
cussions, p. 765. — Ed.
7 Tristia, ii. 348.— Ed.
8 Pseudo-Plato, Epinomis, p. 989.
—Ed.
e Epist, 7.— Ed.
f Stromata, lib. i. p. 275, ed.
Sylb. : A.i5dcrKot3V ns fiavOdvei irXelov,
Kol \4yuiv ffwaKpoarai iroWaKts toIs
iiraKOvovffiv avrov. — Ed.
V IV. 29.— Ed.
d [Crenius, p. 581.] [OabrieViv
NaudcBi Syntagma de Studio Liberali,
Included in tbe Consilia et Methodi
Aureoi studiorum optime instituendo-
rum, collected by Th. Crenius, Kot-
terdam, 1G92. The lines are quoted
as from an anonymous author. —
Ed.]
I Given without author's name, in
LECTURES ON LOGIC. 211
Tliis truth is also well enforced by the Qjreat Vives. lect.
XXXV
" Doctrina est traditio eorum quae quis novit ei qui
non novit. Disciplina est illius traditionis acceptio ; ^'^^^'
nisi quod mens accipientis impletur, dantis vero non
exhauritur, — imo communicatione augetur eruditio,
sicut ignis, motu atque agitatione. Excitatur enim
ingenium, et discurrit per ea quae ad prsesens nego-
tium pertinent ; ita invenit atque excudit multa, et
quae in mentem non veniebant cessanti, docenti aut
disserenti occurrunt, calore acuente vigorem ingenii.
Idcirco, nihil est ad magnam eruditioneni perinde
conducens, ut docere."" The celebrated logician, Dr Sanderson.
Robert Sanderson, used to say : " I learn much from
my master, more from my equals, and most of all
from my disciples."^
But I have occupied perhaps too much time on the influence
influence of the communication of knowledge on those muuication
,,.. , ^^.. -of Know-
by whom it IS made ; and shall now pass on to the lodge on
consideration of its influence on those to whom it is whom it is
addressed. And in treating of communication in
this respect, I shall, in the first place, consider it
as One-sided, and, in the second, as Eeciprocal or
Bilateral.
The Unilateral Communication of knowledge, or i. instmc-
Instruction, is of two kinds, for it is either Oral orand'writ-
Written ; but as both these species of instruction pro-
pose the same end, they are both, to a certain extent,
subject to the same laws.
Oral and Written Instruction have each their pecu-
liar advantages.
In the first place, instruction by the living voice
the Carmimim Proverbialum Loci fi [Reason and Judgment, or Spe-
Communes, Loncl. 1583, p. 17. See cial Remarks of the Life of the Re-
above, p. 206, note i. — Ed. noioned Dr Sanderson, p. 10. Lon-
a De Anima, p. 89. don : 1663,]
212
LECTURES ON LOGIC.
LECT.
XXXV.
Oral in-
struction,
— its ad-
vantages,
a. More
natural,
therefore
more im-
pressive.
Theophras-
tus.
Younger
Pliny.
Valerius
Maximi.s.
St Jerome.
b. Less per-
manent,
therefore
more at-
tended to.
c. Hearing
a social act,
lias this advantage over that of books, that, as more
natural, it is more impressive. Hearing rouses the
attention and keeps it alive far more effectually than
reading. To this we have the testimony of the most
competent observers. " Hearing," says Theophrastus,"
" is of all the senses the most pathetic," that is, it is
the sense most intimately associated with sentiment
and passion. " Multo magis," says the younger
Pliny, " multo magis viva vox afficit. Nam, licet
acriora sunt quae legas, altius tamen in animo sedent
quse pronuntiatio, vultus, habitus, gestus etiam dicen-
tis adfigit." ^
" Plus prodest," says Valerius Maximus, " docentem
audire, quam in libris studere; quia vehementior fit
impressio in mentibus audientium, ex visu doctoris et
auditu, quam ex studio et libro."''^
And St Jerome — " Habet nescio quid latentis ener-
gise viva vox; et in aures discipuli de doctoris ore
transfusa, fortius sonat."^
A second reason why our Attention (and Memory
is always in the ratio of Attention) to things spoken
is greater than to things read, is that what is written
we regard as a permanent possession to which we can
always recur at pleasure; whereas we are conscious
that the "winged words" are lost to us for ever, if we
do not catch them as they fly. As Pliny hath it : —
"Legendi semper est occasio; audiendi non semper."^
A third cause of the superior efiicacy of oral in-
a OvK Uv arjScos 5' ol/xai ae Trpoca-
Kovcrai irepl ttjs aKovffTiKTJs alffdrjfffwi,
^v 6 @f6(ppa<TTos iraQrjTLKiiiraTriv elvai
<pr)<rl iracrwv. Plutarch, De Auditione,
sub init. — Ed.
6 Ejjist., ii. 3.— Ed.
7 [Thomas Hiberiiicus, p. 330.]
[The above passage is quoted as from
Valerius, lib. viii., in the Flores of
Thomas Hibernicus, and in the An-
thologia of Langius, under the article
Doctrina. It is not, however, to be
found in that author. — Ed. ]
S Epist, ciii, OjJera, Antv. 1579,
tom. iii. p. 337.— Ed.
e Ujjist., ii. 3 Ed.
LECTURES ON LOGIC. 218
struction is that man is a social animal. He is thus lect.
naturally disposed to find pleasure in society, and in ^ ^
the performance of the actions performed by those
with whom he consorts. But reading is a solitary,
hearing is a social, act. In reading, we are not deter-
mined to attend by any fellow-feeling with others
attending; whereas in hearing, our attention is not
only engaged by our sympathy with the speaker, but
by our sympathy with the other attentive auditors
around us.
Such are the causes which concur in rendering Menage
Oral Instruction more effectual than Written. "M.
Varillas," says Menage, (and Varillas was one of the
most learned of modern historians, — and Menage one
of the most learned of modern scholars), " M. Varillas
himself told me one day, that of every ten things
he knew, he had learned nine of them in conversation.
I myself might say nearly the same thing.""
On the other hand, Reading, though only a substi- Reading —
tute for Oral Instruction, has likewise advantages lages.'
peculiar to itself. In the first place, it is more easily I'^lly'^^
accessible. In the second, it is more comprehensive ^'"''^j^'^g^^'
in its sphere of operation. In the third, it is not ^?™p^''''^°'
transitory with the voice, but may ao;ain and ap'ain c. More
^ _ ./ o o permanent.
be taken up and considered, so that the object of the
instruction may thus more fully be examined and
brought to proof. It is thus manifest, that oral and
written instruction severally supply and severally sup-
port each other ; and that, where this is competent,
they ought always to be employed in conjunction.
Oral instruction is, however, in the earlier stages
of education, of principal importance ; and written
ought, therefore, at first only to be brought in as a
a Menagiana, torn. iv. p. Ill, ed. 1715. ^Ed.
214! LECTUKES ON LOGIC.
LECT. subsidiary. A neglect of the oral instruction, and an
XXXV •/ cj
L exclusive employment of the written, — the way in
which those who are self-taught (the autodidacti)
obtain their education, — for the most part betrays its
one-sided influence by a contracted cultivation of the
intellect, with a deficiency in the power of communi-
cating knowledge to others.
Oral instruction necessarily supposes a speaker and
a hearer ; and written instruction a writer and a
reader. In these, the capacity of the speaker and of
the writer must equally fulfil certain common requi-
sites. In the first place, they should be fully masters
of the subject with which their instruction is conver-
sant ; and in the second, they should be able and
willing to communicate to others the knowledge which
they themselves possess. But in reference to these
several species of instruction, ther^ are various special
rules that ought to be attended to by those who would
reap the advantages they severally afford. I shall
commence with Written Instruction, and comprise the
rules by which it ought to be regulated, in the follow-
ing paragraph.
Par.cxiii. H CXIII. In regard to Written Instruction,
*» ri ttcii
Instruction, and its profitable employment as a means of in-
aud its em- j_ n j. i • i • i
pioyment tcllectuaJ improvcmcut, there are certain rules
ofinteiiec- which ouglit to bc observed, and which to2;ether
pr'ovement. constituto thc Propcr Method of Eeading. These
may be reduced to three classes, as they regard,
1°, The Quantity, 2°, The Quality, of what is to be
read, or, 3°, The Mode of reading what is to be read.
I. As concerns the Quantity of what is to be
read, there is a single rule,— Read much, but
not many works (multum non multa).
LECTURES ON LOGIC. 215
II. As concerns the Quality of what is to be lect.
\xxv
read, — there may be given five rules. 1°, Select '-
the works of principal importance, estimated by
relation to the several sciences themselves, or to
your particular aim in reading, or to your indi-
vidual disposition and wants. 2°, Eead not the
more detailed works upon a science, until you
have obtained a rudimentary knowledge of it in
general. 3°, Make yourselves familiar with a
science in its actual or present state, before you
proceed to study it in its chronological develop-
ment. 4°, To avoid erroneous and exclusive
views, read and compare together the more im-
portant works of every sect and party. 5°, To
avoid a one-sided development of mind, combine
with the study of works which cultivate the
Understanding, the study of works which culti-
vate the Taste.
III. As concerns the Mode or Manner of read-
ing itself, there are four principal rules. 1°,
Read that you may accurately remember, but
still more, that you may fully understand. 2°,
Strive to compass the general tenor of a work,
before you attempt to judge of it in detail. 3°,
Accommodate the intensity of the reading to the
importance of the work. Some books are, there-
fore, to be only dipped into; others are to be run
over rapidly ; and others to be studied long and
sedulously. 4°, Eegulate on the same principle
the extracts which you make from the works you
read."
a. Cf. Krug, Logih, § 180.— Ed. § 53, p. 196 ; 1832. Magirus Flori-
[Fischaber, Logik, p. 188, ed. 1818. legium, v. Lectio.']
Scheidler, Grundriss der Hodegctih,
216
LECTUHES ON LOGIC.
LECT.
XXXV.
Explica-
tion.
I. Quantity
to be read.
Rule.
Solomon,
Quintilian.
Younger
Pliny.
Seneca.
Luther
quoted.
Sanderson.
I. In reference to the head of Quantity, the single
rule is — Eead much, but not many works. Though
this golden rule has risen in importance, since the
world, by the art of printing, has been overwhelmed
by the multitude of books, it was still fully recog-
nised by the great thinkers of antiquity. It is even
hinted by Solomon, when he complains that " of mak-
ing many books there is no end."" By Quintilian,
by the younger Pliny, and by Seneca, the maxim —
" multum legendum esse, non multa " — is laid down
as the great rule of study.^ " All," says Luther
in his Table Talk,'^ " who would study with advan-
tage in any art whatsoever, ought to betake them-
selves to the reading of some sure and certain books
oftentimes over; for to read many books produceth
confusion, rather than learning, like as those who
dwell everywhere, are not anywhere at home." He
alludes here to the saying of Seneca, " Nusquam est
qui ubique est."^ "And like as in society, we use
not daily the community of all our acquaintances,
but of some few selected friends, even so likewise
ought we to accustom ourselves to the best books,
and to make the same familiar unto us, that is, to
have them, as we use to say, at our lingers' ends."
The great logician, Bishop Sanderson, to whom I for-
merly referred, as his friend and biographer Isaac A¥al-
ton informs us, said " that he declined reading many
books ; but what he did read were well chosen, and
read so often that he became very familiar with them.
They were principally three, — Aristotle's Rhetoric,
Aquinas's Secunda Secundce, and Cicero, particularly
I
a Eccles. xii. 12.— Ed.
/3 Quintilian, x. 1, 59. Pliny,
Ep., vii. 9. Seneca, De TranquUl.
Animi, c. 9; Ejnst., 2, 45. — Ed.
7 No. DCCCXLiv. Of Learned Men.
-Ed.
8 Ejnst., ii.— Ed.
LECTUEES ON LOGIC. 217
his Offices.""' The great Lord Burleigh, we are told lect.
by his biographer, carried Cicero De Officiis, with
Aristotle's Rhetoric, always in his bosom ; these being J^?^^ ^^■
complete pieces, " that would make both a scholar and
an honest man." " Our age," says Herder, " is the Herder.
reading age ; " and he adds, " it would have been
better, in my opinion, for the world and for science,
if, instead of the multitude of books which now over-
lay us, we possessed only a few works good and ster-
ling, and which, as few, would, therefore, be more
diligently and profoundly studied."^ I might quote
to you many other testimonies to the same effect ;
but testimonies are useless in support of so manifest
a truth.
For what purpose, — with what intent, do Ave read 1 Eud of
We read not for the sake of reading, but we read to
the end that we may think. Heading is valuable
only as it may supply to us the materials which
the mind itself elaborates. As it is not the largest
quantity of any kind of food, taken into the stomach,
that conduces to health, but such a quantity of such
a kind as can be best digested ; so it is not the
greatest complement of any kind of information that
improves the mind, but such a quantity of such a
kind as determines the intellect to most vigorous
energy. The only profitable reading is that in which
we are compelled to think, and think intensely ;
whereas that reading which serves only to dissipate
and divert our thought, is either positively hurtful,
or useful only as an occasional relaxation from severe
exertion. But the amount of vigorous thinking is
a See Walton's Lives of Donne, fi Briefe iiber das Stud, der Theol.
Wotto7i, Hooker, Herbert, and San- B. xlix., Werlce, xiv. 267, ed. 1829.
derson, vol. ii. p. 287, ed. Zouch, — Ed.
York, 1817.— Ed.
First Rule.
218 LECTUEES ON LOGIC.
LECT. usually in the inverse ratio of multifarious readius;.
XXXV • • • •
'- Multifarious reading is agreeable; but, as a habit, it
is, in its way, as destructive to the mental as dram-
drinking is to the bodily health.
IT. Quality II. In reference to the Quality of what is to be read,
to be read, thc First of tho five rules is — ' Select the Avorks of prin-
cipal importance, in accommodation either to the seve-
ral sciences themselves, to your particular aim in read-
ing, or to your individual disposition and wants.' This
rule is too manifestly true to require any illustration
of its truth. No one will deny that for the accom-
plishment of an end, you ought to employ the means
best calculated for its accomplishment. This is all
that the rule inculcates. But while there is no diffi-
culty about the expediency of obeying the rule, there
is often considerable difficulty in obeying it. To know
what books ought to be read in order to learn a science,
is in fact frequently obtained only after the science has
been already learned. On this point no general advice
can be given. We have, on all of the sciences, works
which profess to supply the advice which the student
here requires. But in general, I must say, they are of
small assistance in pointing out what books we should
select, however useful they may be in showing us what
books exist upon a science. In this respect, the British
student also labours under peculiar disadvantages.
The libraries in this country are, one and all of them,
wretchedly imperfect ; and there are few departments
of science, in which they are not destitute even of the
works of primary necessity, — works which, from their
high price, but more frequently from the difficulty
of procuring them, are beyond the reach of ordinary
readers.
Under the head of Quality the Second Rule is —
LECTURES ON LOGIC. 219
' Read not the more detailed works upon a science, lect.
until you have obtained a rudimentary knowledge oi
it in general.' The expediency of this rule is suffi- Rule,
ciently apparent. It is altogether impossible to read
with advantage an extensive work on any branch of
knowledge, if we are not previously aware of its general
bearing, and of the relations in which its several parts
stand to each other. In this case, the mind is over-
powered and oppressed by the mass of details pre-
sented to it, — details, the significance and subordina-
tion of which it is as yet unable to recognise. A con-
spectus,-^a survey of the science as a whole, ought,
therefore, to precede the study of it in its parts ; we
should be aware of its distribution, before we attend
to what is distributed, — we should possess the empty
frame-work, before we collect the materials with which
it is to be filled. Hence the utility of an encyclo-
paedical knQwledge of the sciences in general, prelimi-
nary to a study of the several sciences in particular;
that is, a summary knowledge of their objects, their
extent, their connection with each other. By this
means the student is enabled to steer his way on the
wide ocean of science. By this means he always knows
whereabouts he is, and becomes aware of the point
towards which his author is leading him.
In entering upon the study of such authors as Plato,
Aristotle, Descartes, Spinoza, Leibnitz, Locke, Kant,
&c., it is, therefore, proper that we first obtain a pre-
paratory acquaintance with the scope, both of their
philosophy in general, and of the particular work on
which we are about to enter. In the case of writers
of such ability this is not difiicult to do; as there are
abundance of subsidiary works, affording the prelimi-
nary knowledge of which we are in quest. But in the
ii
220 LECTURES ON LOGIC.
LECT, case of treatises wliere similar assistance is not at band,
XXXV
1 '- we may often, in some degree, prepare ourselves for a
regular perusal, by examining tbe table of contents,
and taking a cursory inspection of its several depart-
ments. In this respect and also in others, the follow-
ing advice of Gibbon to young students is highly de-
Gibbon serving of attention. " After a rapid glance (I trans-
late from the original French) — after a rapid glance
on the subject and distribution of a new book, I sus-
pend the reading of it, which I only resume after hav-
ing myself examined the subject in all its relations,
— after having called up in my solitary walks all that
I have read, thought, or learned, in regard to the sub-
ject of the whole book, or of some chapter in particu-
lar. I thus place myself in a condition to estimate
what the author may add. to my general stock of know-
ledge; and I am thus sometimes favourably disposed
by the accordance, sometimes armed by the opposition,
of our views.""
Third Xhe Third Eule under the head of Quality is —
Rule. ''
' Make yourselves familiar Avith a science in its present
state, before you proceed to study it in its chronologi-
cal development.' The propriety of this procedure is
likewise manifest. Unless we be acquainted with a
science in its more advanced state, it is impossible to
distinguish between what is more or less important,
and, consequently, impossible to determine what is or
is not worthy of attention in the doctrines of its earlier
cultivators. We shall thus also be overwhelmed by,
the infinitude of details successively presented to us ;
all will be confusion and darkness, where all ought to
a The substance of the above pas- pp. 54, f)5 ; ed. 1837. The French;
sage is given in English, in Gibbon's original is quoted by Scheidler, Ho-,
Memoirs of iny Life and Writings, degetik, § 55, p. 204. — Ed.
LECTURES ON LOGIC. 221
be order and light. It is thus improper to study lect.
philosophy historically, or in its past progress, be- - — ^ — '-
fore we have studied it statistically, or in its actual
results.
The Fourth Kule under the same head is — ' To Fourth
avoid erroneous and exclusive views, read and com-
pare together the more important works of every party.'
In proportion as different opinions may be entertained
in regard to the objects of a science, the more neces-
sary is it that we should weigh with care and imparti-
ality the reasons on which these different opinions rest.
Such a science, in particular, is philosophy, and such
sciences, in general, are those which proceed out of
philosoph}^ In the philosophical sciences, we ought,
therefore, to be especially on our guard against that
partiality which considers only the arguments in favour
of particular opinions. It is true that in the writings
of one party we find adduced the reasons of the oppo-
site party; but frequently so distorted, so mutilated,
so enervated, that their refutation occasions little
effort. We must, therefore, study the arguments on
both sides, if we would avoid those one-sided and con-
tracted views which are the result of party-spirit.
The precept of the Apostle, " Test all things, hold fast
by that which is good," is a precept which is applicable
equally in philosophy as in theology, but a precept
that has not been more frequently neglected in the
one study than in the other.
The Fifth Eule under the head of Quality is — ' To Fifth Rule,
avoid a one-sided development of mind, combine with
the study of works which cultivate the Understanding,
the study of works which cultivate the Taste.' The
propriety of this rule requires no elucidation.
I therefore, pass on to the third head — viz. the
222 LECTURES OX LOGIC.
LECT. Manner of readine: itself: under which the First
XXXV
Rule is — ' Eead that you may accurately remem-
of ReadrngT bcr, but stlll Hiorc that you may fully understand.'
u e. rpi^-g ^|g^ requires no comment. Reading should not
be a learning by rote, but an act of reflective think-
ing. Memory is only a subsidiary faculty, — is valuable
merely as supplying the materials on which the under-
standing is to operate. We read, therefore, principally,
not to remember facts but to understand relations.
To commit, therefore, to memory what we read, before
we elaborate it into an intellectual possession, is not
only useless but detrimental ; for the habit of laying
up in memory what has not been digested by the
understanding, is at once the cause and the effect of
mental weakness.
Second The Second Rule under this head is — ' Strive to
compass the general tenor of a work, before you at-
tempt to judge of it in detail.' Nothing can be more
absurd than the attempt to judge a part, before com-
prehending the whole; but unfortunately nothing is
more common, especially among professional critics, —
reviewers. This proceeding is, however, as frequently
the effect of wilful misrepresentation, as of uninten-
tional error.
Third Rule. The Third Rule under this head is — 'Accommodate
the intensity of the reading to the importance of the
work. Some books are, therefore, to be only dipped
into ; others are to be run over rapidly ; and others
to be studied long and sedulously.^ All books are not
to be read with the same attention ; and, accordingly, ;
Lectio cur- au ancicut distinction was taken of reading into lectio !
Lectio sta- cursoTia and lectio stataria. The former of these
we have adopted m English, cursory readmg bemg ;
a familiar and correct translation of lectio cursoria. i
LECTURES ON LOGIC. 223
Bat lectio stataria cannot be so well rendered by the lect.
expression of stationary reading. " Eead not," says
Bacon in his Fiftieth Essay — " read not to contradict q^Ted.
and confute, nor to believe and take for granted, nor
to find talk and discourse, but to weigh and consider.
Some books are to be tasted, others are to be swallowed,
and some few to be chewed and digested ; that is,
some books are to be read only in parts ; others to be
read, but not curiously ; and some few to be read
wholly and with diligence and attention. Some books
also may be read by deputy, and extracts made of
them by others ; but that would be only in the less
important arguments, and the meaner sort of books ;
else distilled books are, like common distilled waters,
fleshy things/' " One kind of books," says the great
historian, Johann von Mtiller,'' "I read with great Johann von
rapidity, for in these there is much dross to throw
aside, and little gold to be found ; some, however, there
are all gold and diamonds, and he who, for example,
in Tacitus can read more than twenty pages in four
hours, certainly does not understand him."
Eapidity in reading depends, however, greatly on
our acquaintance with the subject of discussion. At
first, upon a science we can only read with profit few
books, and laboriously. By degrees, however, our
knowledge of the matters treated expands, the reason-
ings appear more manifest, — we advance more easily,
until at length w^e are able, without overlooking any-
thing of importance, to read with a velocity which
appears almost incredible for those who are only
commencing the study.
The Fourth Kule under this head is — ' Reo;ulate on Fourth
° Rule.
a Werhe, iv. 177. Cf. xvii. 253. 55, p. 204.— Ed.
Quoted by Scheidler, Hodegetik, §
224 LECTURES ON LOGIC.
LECT. the same principle the extracts which you make from
^ L the works you read.'
So much for the Unilateral Communication of
thought, as a mean of knowledge. We now proceed
to the Mutual Communication of thought, — Confer-
ence.
Conference, This is either mere Conversation, — mere Dialoo;ue,
—of two ' . ^ ,^ -
kinds. or Formal Dispute, and at present we consider both
of these exclusively, only as means of knowledge, —
only as means for the communication of truth.
1. Dialogue. The employment of Dialogue as such a mean, re-
quires great skill and dexterity ; for presence of mind,
confidence, tact, and pliability are necessary for this,
and these are only obtained by exercise, independently
of natural talent. This was the method which Socra-
tes almost exclusively employed in the communication
of knowledge ; and he called it his art of intellectuah
midwifery, because in its application truth is not given
over by the master to the disciple, but the master, by
skilful questioning, only helps the disciple to deliver
himself of the truth explicitly, which his mind had
before held implicitly. This method is not, however,
applicable to all kinds of knowledge, but only to those
which the human intellect is able to evolve out of it-
self, that is, only to the cognitions of Pure Keason.
2. Disputa- Disputation is of two principal kinds, inasmuch as it
and Writ- is Oral or written ; and in both cases, the controversy
may be conducted either by the rules of strict logical
disputation, or left to the freedom of debate. With-
out entering on details, it may be sufficient to state, in
Academical regard to Logical Disputation, that it is here essential
disputation. , , . . i • j i
that the point m question, — the status controversice, —
the thesis, should, in the first place, be accurately de-
termined, in order to prevent all logomachy, or mere
LECTURES ON LOGIC. 225
who denies the thesis, aud who is called the opponent, lect.
may either call upon the disputant who affirms the '-
thesis, and who is called the defendant, to allege an
argument in its support, or he may at once himself
produce his counter-argument. To avoid, however, all
misunderstanding, the opponent should also advance
an antithesis, that is, a proposition conflictive with the
thesis, and when this has been denied by the defend-
ant the process of argumentation commences. This
proceeds in regular syllogisms, and is governed by
definite rules, which are all so calculated that the dis-
cussion is not allowed to wander from the point at
issue, and each disputant is compelled, in reference to
every syllogism of his adversary, either to admit, or
to deny, or to distinguish." These rules you will find
in most of the older systems of Logic ; in particular
I may refer you to them as detailed in Heerebord's
Praxis Logica, to be found at the end of his edition
of the Synopsis of Burgersdicius. The practice of
disputation was long and justly regarded as the most
important of academical exercises ; though liable to
abuse, the good which it certainly ensures greatly sur-
passes the evil which it may accidentally occasion.
a Cf. Krug, Lorjil; § 186. Aum. 2. Scheidler, Hodegetll; § 45, p. 138- Ed.
VOL. IL
APPENDIX.
APPENDIX.
I.
THE CHARACTER AND COMPREHENSION OF LOGIC.
—A FRAGMENT.
(See above, Volume I., page 4.)
In the commencement of a course of academical instruction, there
are usually two primary questions wliich obtrude themselves ;
and with the answer to these questions I propose to occupy the
present Lecture.
The first of these questions is, — AVhat is the character and
comprehension of the subject to be taught ? The second, — What
is the mode of teaching it ? In regard to the former of these, the
question, — What is to be taught, — in the present instance is as-
suredly not superfluous. The subject of our course is indeed pro-
fessedly Logic ; but as under that rubric it has been too often the
practice, in our Scottish Universities, to comprehend almost every
thing except the science which that name properly denotes, it is
evident that the mere intimation of a course of Lectures on Logic
does not of itself definitely mark out what the professor is to
teach, and what the student may rely on learning.
I shall, therefore, proceed to give you a general notion of what
Logic is, and of the relation in which it stands to the other
sciences, for Logic, — Logic properly so called, — is the all-import-
ant science in which it is at once my duty and my desire fully
and faithfully to instruct you.
The very general, — I may call it the very vague, — conception
which I can at present attempt to shadow out of the scope and na-
ture of Logic, is of course not intended to anticipate what is here-
after to be articulately stated in regard to the peculiar character
of this science.
230 APPENDIX.
All science, all knowledge, is divided into two great branches ;
for it is either, 1°, Conversant about Objects Known, or, 2°, Con-
versant about the Manner of knowing them, in other words, about
the laws or conditions under which such objects are cognisable.
The former of these is Direct Science, or Science simply; the
latter, Keflex Science, — the Science of Science, or the Method of
Science.
Now of these categories or great branches of knowledge, Simple
Science, or Science directly conversant about Objects, is again
divided into two branches ; for it is either conversant about the
phsenomena of the internal world, as revealed to us in conscious-
ness, or about the phsenomena of the external world, as made
known to us by sense. The former of these constitutes the
Science of Mind, the latter the Science of Matter ; and each is
again divided and subdivided into those numerous branches, which
together make up nearly the whole cycle of human knowledge.
The other category, — the Science of Science, or the Method-
ology of Science, — falls likewise into two branches, according as the
conditions which it considers are the laws which determine the
possibility of the mind, or subject of science, knowing, or the
laws which determine the possibility of the existence, or ob-
ject of science, being known ; Science, I repeat, considered as
reflected upon its own conditions, is twofold, for it either con-
siders the laws under which the human mind can know, or the
laws under which what is proposed by the human mind to know,
can be known. Of these two sciences of science, the former, —
that which treats of those conditions of knowledge which lie in
the nature of thought itself, — is Logic, properly so called ; the
latter, — that which treats of those conditions of knowledge which
lie in the nature, not of thought itself, but of that which we
think about, — this has as yet obtained no recognised appellation,
no name by which it is universally and familiarly known. Vari-
ous denominations have indeed been given to it in its several parts
or in its special relations ; thus it has been called Heuretic, in so
far as it expounds the rules of Invention or Discovery, Architec-
tonic, in so far as it treats of the method of building up our ob-
servations into system ; but hitherto it has obtained, as a whole,
no adequate and distinctive title. The consequence, or perhaps
the cause, of this want of a peculiar name to mark out the second
APPENDIX. 231
science of science, as distinguished from the first, is that the two
have frequently been mixed up together, and that the name of
Logic has been stretched so as to comprehend the confused assem-
blage of their doctrines. Of these two sciences of the conditions
of knowledge, — the one owes its systematic development prin-
cipally to Aristotle, the other to Bacon ; though neither of
these philosophers has precisely marked or rigidly observed the
limits which separate them from each other ; and from the cir-
cumstance, that the latter gave to his great Treatise the name of
Organum, — the name which has in later times been applied to
designate the complement of the Logical Treatises of the former
— from this circumstance, I say, it has often been supposed, that
the aim of Bacon was to build up a Logic of his own upon the
ruins of the Aristotelic. Nothing, however, can be more errone-
ous, either as to Bacon's views, or as to the relation in which the
two sciences mutually stand. These are not only not mconsistent,
they are in fact, as correlative, each necessary to, each dependent
on, the other ; and although they constitute two several doctrines,
which must be treated in the first instance each by and for itself,
they are, however, in the last resort only two phases, — two mem-
bers, of one great doctrine of method, which considers, in the
counter relations of thought to the object, and of the object to
thought, the universal conditions by which the possibility of hu-
man knowledge is regulated and defined.
But allowing the term Logic to be extended so as to denote the
genus of which these opposite doctrines of Method are the species,
it will, however, be necessary to add a difference by which these
special Logics may be distinguished from each other, and from the
generic science of which they are the constituents. The doctrine,
therefore, which expounds the laws by which our scientific pro-
cedure should be governed, in so far as these lie in the forms of
thought, or in the conditions of the mind itself, which is the sub-
ject in which knowledge inheres, — this science may be called For-
mal, or Subjective, or Abstract, or Pure Logic. The science, again,
which expounds the laws by which our scientific procedure should
be governed, in so far as these lie in the contents, materials, or ob-
jects, about which knowledge is conversant, — this science may be
called Material, or Objective, or Concrete, or Applied Logic.
Now it is Logic, taken in its most unexclusive acceptation
S32 APPENDIX.
which will constitute the object of our consideration in the follow-
ing course. Of the two branches into which it falls, Formal Logic,
or Logic Proper, demands the principal share of our attention, and
this for various reasons. In the first place, considered in reference
to the quantity of their contents. Formal Logic is a far more com-
prehensive and complex science than Material. For, to speak first
of the latter : — if we abstract from the specialities of particular
objects and sciences, and consider only the rules which ought to
govern our procedure in reference to the object-matter of the sci-
ences in general, — and this is all that a universal Logic can pro-
pose, — these rules are few in number, and their applications simple
and evident. A Material or Objective Logic, except in special
subordination to the circumstances of particular sciences, is, there-
fore, of very narrow limits, and all that it can tell us is soon told_
Of the former, on the other hand, the reverse is true. For though
the highest laws of thought be few in number, and though Logic
pro2:)er be only an articulate exposition of the universal necessity
of these, still the steps through which this exposition must be ac-
complished, are both many and multiform.
In the second place, the doctrines of Material Logic are not
only far fewer and simpler than those of Formal Logic, they are
also less independent ; for the principles of the latter, once estab-
lished, those of the other are either implicitly confirmed, or the
foundation laid on which they can be easily rested.
In the third place, the study of Formal Logic is a more improv-
ing exercise ; for, as exclusively conversant with the laws of thought,
it necessitates a turning back of the intellect upon itself, which is
a less easy, and, therefore, a more invigorating, energy, than the
mere contemplation of the objects directly presented to our observa-
tion.
In the fourth place, the doctrines of Formal Logic are possessed
of an intrinsic and necessary evidence, they shine out by their
native light, and do not require any proof or corroboration beyond
that which consciousness itself supplies. They do not, therefore,
require, as a preliminary condition, any apparatus of acquired
knowledge. Formal Logic is, therefore, better fitted than Material,
for the pm-poses of academical instruction ; for the latter, primarily
conversant with the conditions of the external world, is in itself a
less invigorating exercise, as determining the mind to a feebler and
APPENDIX. 233
more ordinary exertion, and, at the same time, cannot adequately
be understood without the previous possession of such a comple-
ment of information, as it would be unreasonable to count upon in
the case of those who are only commencing their philosophical
studies.
II.
GENUS OF LOGIC.
(See above, Vol. I., p. 9.)
I. — SCIENCE.
A. Affirmative.
Stoici, (v. Alexander Aphrod. In Topica, Prooem. ; Diogenes
Laertius, Vita Zenonis, L. vii., § 42). "Plato et Platonici et
Academici omnes," (v. Camerarius, Selectee Dispiit Philos. Pars.
i., qu. 3, p. 30).
(«)— SPECULATIVE SCIENCE.
Toletus, In Un. Arist. Log., De Dial, in Communi, Qu. ii., iv.
Suarez, Disp. Metaph.., Disp. i. § iv. 26 ; Disp. xliv. § xiii. o-i.
"Communiter Thomistse, ut Capreolus, Sotus, Masius, Flandra,
Soncinas, Javellus : Omnes fere Scotistse cum Scoto, ut Valera,
Antonius Andreas, &c." (v. Ildephonsus de Penafiel, Logicce Dis-
putationes, Disp. i. qu. 4. Cursus, p. 79.) For Aquinas, Dm-andus,
Niphus, Canariensis, see Antonius Ruvio, Co7n. in Arist. Dialect,
Prooem. qu. 5. For Bacchonus, Javellus, Averroes, see Conimbri-
censes, In Arist. Dial. Prooem. Q. iv. art. 5. Lalemandet, Cur-
sus PJiil, Logica, Disp. iii. part iii. Derodon, Logica Restit., De
Genere, p. 4.5. Camerarius, Disp. Phil., Pars i., qu. 3, 4. (That Lo-
gica docens a true science). For Pseudo-Augustinus, Avicenna,
Alpharabius, see Conimbricenses, Com. in Arist. Dial. Prooem. Qu.
iv. art. 3. For Boethius, Mercado, Vera Cruce, Montanesius, see
Masius, Co7n. in Porpli. et in Universam Aristotelis Logicanij
Sect, i., Prooem. qu. v. et seq. Poncius, De Nat. Log., Disp. ii.,
concl. 2. For Rapinseus, Petronius, Faber, see Camerarius, Sel.
Disp. Phil, Pars i., qu. 4, p. 44.
234 APPENDIX.
(6) — PRACTICAL SCIENCE.
Conimbricenses, In Univei'sam Aristotelis Dialecticam
Prooem. Qu. iv., art 5. Fonseca, In Iletaph. L. ii. c. 3, qu.
1, § 7. For Venetus, Albertus Magnus, Jandunus, see Ruvio,
I. c. Schiller, Philosophia nova Methodo Explicata. Pars Prior,
L. V. ex. i., p. 306. (1603). D'Abra de Raconis, Summa Totius
Philosophice, Log. Prcel, c. i. Isendoorn, Cursiis Logicus, L.
i., c. 2, qu. 7. Biel, In Sentent., L. ii. Prol. Occam, Summa
Totius Logicce, D. xxxix. qu. 6. For Aureolus, Bern. Mirandulanus
see Conimbricenses, I. c. For Mathisius, Murcia, Vasquez, Eckius,
see Camerarius, Sel. Disp. Phil. Pars, i., qu. 4, p. 44. Ildephon-
sus de Penafiel, Log. Disp. D. i. qu. 4, sect. 2. Oviedo, Cursus
Philosophicus, Log., Contr. Prooem. ii. 5. Arriaga, Cursus Philo-
sophicus, Disp. iii. § 4.
(c) — SPECULATIVE AND PRACTICAL.
Hurtado de Mendoza, Log. Disp. D. ii. § 2.
B. Negative.
For almost all the Greek commentators, see Zabarella, Opera
Logica, De Nat. Log., L. i. c. 5, and Smiglecius, Logica, D. ii. qu. 5.
See also Ildephonsus de Penafiel, Disp. Log. D. i. qu. 1, § 1, p. 67.
II. — ART.
Scheibler, Opera Logica, Pars, i, c. 1, p. 49. J. C. Scaliger,
Exercitationes, Exerc. i. 3. G. J. Vossius, De Natura Artium,
L. iv., c. 2, § 4. Balforeus, In Org. Q. v. § 6, Prooem., p. 31.
Burgersdicius, Institutiones Logicce. Lib. i. c. 1. Pacius, Comm.
in Org. p. 1. Sanderson, Log. Artis Compendium, L. i. c. 1, p. 1,
Cf. p. 192. Aldrich, Artis Log. Compendium. L. i. c. 1, p. 1.
Hildenius, Qumstiones et Commentaria in Organon, p. 579 (1585.)
Goclenius, Prohlemata Logica et Philosophica. Pars. i. qu. 3.
Ramus, Dialectica. L. i. c. 1. Augustinus, De Ordine, ii. c. 15.
Cicero, De Claris Oratoribus, c. 41. De Oratore, L. ii., c. 38.
APPENDIX. 235
Lovanienses, Com. in Arist. Dial. Prsef. p. 3. Rodolphus Agricola,
De DialecticcB Inventione, L. ii. p. 255. Monlorius, (Bapt.),
Comm. in Anal. Pr. PrsBf. Nunnesius, De Constitut. Dial., p. 43.
Downam, (Ramist), Comm. in Ram. Dial., L. i. c. 1 , p. 3. Paraeus,
Ars Logica, p. 1, 1670. Por Horatius Coruachinus, Ant. Bernardus
Mirandulanus, Plamminius Nobilius, see Camerarius, Sel. Disp.
Phil Pars. i. q. 3, p. 30.
III.— SCIENCE AND ART.
Lalemandet, Log., Disp. iii. Part iii. cl, 4. (Logica utens, an
art ; Logica docens, a speculative science.) Tartaretus, In P.
Hispanum, f. 2, (Practical Science and Art.) P. Hispanus, Copu-
lata Omn. Ti^actat. Pet. Hisp. Parv. Logical. T. i. f. 10, 1490.
Philosophia Vetus et Kova in Regia Burgundia dim Pertractata,
Logica, T. I., pp. 58, 59. 4tli ed. London, 1685. Tosca, Comp.
Phil. Log., Tr. i. 1. iv. c. 4, p. 208, (Practical Science and Art).
Purchot, Instil. Phil., T. I. Prooem. p. 36. Eiigenius, AoytK-r), pp.
140, 141. Dupleix, Zo^igwe, p. 37. ^SiCciol^iii, RudimentaLogicce,
p. 5. Schmier, Philosophia Quadripartita, (v. Heum annus, j4cto
Philosoph., iii. p. 67.) Aquinas (in Caramuel, Phil. Realis et
Rationalis, Disp. ii. p. 8).
IV. — NEITHER SCIENCE NOR ART, BUT INSTRUMENT, ORGAN, OR
HABIT, OR INSTRUMENTAL DISCIPLINE.
Pliiloponus, In An. Prior., initio. For Animonius, {Prcef. in
Prced.), Alexander, (In Topica, i. c. 4 ; Metaph. ii. t. 15).
Simplicius, (Prcef. in Priced.), Zabarella, {De Notura Logicce, L.
i. c. 10.), Zimara, (In Tabida v. Ahsurdum^, Averroes, see
Smiglecius, Logica, Disp, ii. qu. 6, p. 89. Aegidius, In An. Post.
L. i. qu. 1. For Magnesius, Niger (Petrus), Villalpandeus, see
Ruvio, In Arist. Dial., prooem. qu. 2. F. Crellius, Isagoge Lo-
gica, L. i. c. 1. p. 5. P. Vallius, Logica, T. I. prooem. c. i. et alibi.
Bartholinus, Janitores Logici, II. pp. 25 and 76. Bertius, Logica
Peripatetica, pp. 6, 10. Themistius, An. Post. i. c. 24. Aquinas,
Opuscula, 70, qu. De Divisione Scientim Specidativce, — sed alibi
scientiam vocat. (See Conimbricenses, I71 Arist. Dial., T. I. qu.
236 APPENDIX.
iv. art. 5, p. 42). Balduimis, In Qiicesito an Logica sit Scientia.
Scaynus, Paraphrasis in Org anon. Prsef. p. 9.
V. — THAT, LOOSELY TAKING THE TERMS, LOGIC IS EITHER ART,
OR SCIENCE, OR BOTH.
Zabarella, Opera Logica, De Nat. Log., L. i. c. viii. D'Abra
de Eaconis, Summa Tot. Phil. Prcel. Log., L. iii., c. 1, p. 8, ed.
Colon., (Practical Science), Balforeus, In Organon, Q. v. §§ 1, 6,
pp. 20, 32. (Art). Derodon, Logica Restit. De Prooem. Log.,
p. 49, (Speculative Science). Crellius, Isagoge, pp. 1, 4. Bertius,
Logica Peripatetica, pp. 11, 13. Aldrich, Art. Log. Comp., L. ii.
c. 8, T. i. (Art). Sanderson, Log. Art. Comp. Append. Pr., c. 2,
p. ] 92. (Art). Conimbricenses, InArist. Dial., T. I., p. 33. (Practi-
cal Science). Philosophia Burgundia, T. I. pp. 56, 59. Eustachius,
Summa Philosophia', Dialectica, Qucest. Prooem., i. p. 4. Nim-
nesius, De Constit. Dial., ff. 43, 68. Scheibler, Opera Logica,
pp. 48, 49. Scaynus, Par. in Org., pp. 11, 12. Camerarius, Sel.
Disp. Phil., Pars. i. qu. 3, pp. 81, 38 (Speculative Science). B.
Pereira, De Commun. Princip. Omn. Per. Katural., L. i. De Phil.
c. 18, p. 60, 1618.
VI. — THAT AT ONCE SCIENCE (PART OF PHILOSOPHY) AND
INSTRUMENT OF PHILOSOPHY.
BoetMus, Prcef. in Porphyr. (a Victorino Transl.) Opera, p. 48.
Eustachius, Summa Philosopliice, p. 8, (Scientia organica et prac-
tica.) For Simplicius, Alexander, Philoponus, &c., see Camerarius,
Sel. Disp. Phil., p. 30. Pacius, Com. in Arist. Org., p. 4.
VII. — THAT QUESTION, WHETHER LOGIC PART OF PHILOSOPHY
OR NOT, AN IDLE QUESTION.
Pacius, Com. in A7'ist. Org., p. 4. Avicenna, (in Conimbri-
censes, In Arist. Dial, Qu. iv. art. 4, T. I. p. 38.)
APPENDIX. 237
Vlll. — THAT QUESTION OF WHETHER ART, SCIENCE, &C., IDLE
— ONLY VERBAL.
Buffier, Gours des Sciences^ Seconde Logique, § 421, p. 887.
Eugenius, 'H AoytKi), p. 140, has the following : —
" Prom what has been said, therefore, it clearly appears of what
character are the diversities of Logic, and what its nature. For
one logic is Natural, another Acquired. And of the Natural,
there is one sort according to Faculty, another according to Dis-
position. And of the Acquired, there is again a kind according to
Art, and a kind according to Science. And the Native Logic,
according to Faculty, is the rational faculty itself with which every
human ^individual is endowed, through which all are qualified for
the knowledge and discrimination of truth, and which, in propor-
tion as a man employs the less, the less is he removed from irra-
tionality. But the Native Logic, according to Disposition, is the
same faculty by which some, when they reason, are wont to exert
their cogitations with care and attention, confusedly, indeed, and
uncritically, still, however, in pursuit of the truth. The Acquired,
according to Art, is the correct and corrected knowledge of the
Ptules, through which the intellectual energies are, without fault
or failure, accomplished. But the Acquired, according to Science,
is the exact and perfect knowledge both of the energies themselves,
and also of the causes through which, and through which exclu-
sively, they are capable of being directed towards the truth."
[ Native, according to j j^-'posftion.
Logic. <
f Acquired, according to < rj • '
^ ^ ' ( Science.
" And thus Disposition adds to Faculty consuetude and a
promptness to energise. Art, again, adds to Disposition a refine-
ment and accuracy of Energy. Finally, Science adds to Art the
consciousness of cause, and the power of rendering a reason in the
238 APPENDIX.
case of all the Rules. And the natural logician may be able, in his
random reason, to apprehend that, so to speak, one thing has de-
termined another, although the nature of this determination may
be beyond his ken. But he whose disposition is exercised by re-
flection and imitation, being able easily to connect thought with
thought, is cognisant of the several steps of the reasoning process,
howbeit this otherwise may be confused and disjointed. But he
who is discipKned in the art, knows exactly that, in an act of infer-
ence, there are required three terms, and that these also should be
thus or thus connected. Finally, the scientific logician under-
stands the reason, — why three terms enter into every syllogism, —
why there are neither more nor fewer, — and why they behove to
be combined in this, and in no other fashion.
" Wherefore to us the inquiry appears ridiculous, which is fre-
quently, even to nausea, clamorously agitated concerning Logic —
Whether it should be regarded as an Art or as a Science."
APPENDIX.
239
III.
DIVISIONS, VAEIETIES, AND CONTENTS OF
LOGIC.
(See above, Vol. I., p. 68.)
1. LOGICA, <
Docens,
X^piy ■KpayiJ.a.Twv,
Utens,
iv xp'^'^^^ '"*^ yv/xvacria
■Kpa.yfx.aTwv,
f\. Timpler, Logicce Systema, L. i. c.
i. qusest. 2, 3. Isendoom, Effata,
Centuria, i. Eff. 55. Crellius,
Isagoge, Pars Prior, L. i. c. i. p. 12.
Noldius, Logica Recognita, Prooem.
p. 13.
Philoponus, In. An. Pr., f. 4. Al-
steclius, Encyclopcedia, pp. 29 and
406. V. Aristotle, Aletaph., L. vii.
text, 23.
II. Logica,
Doctrinalis ) [Objec-
Systematica ) tiva],
Habitualis,[Subjectiva],
V. Timpler, Syst. Log., Appendix, p.
877. Noldius, Log. Recog., Prooem.,
p. 13.
III. Logica, ,
Pars Communis, Gene
ralis, ^
Pars Propria, Specialis,
adopted in dififerent significations by
Timpler, Syst. Log., q. 19, p. 55.
Theoph. Gale, Logica, pp. 6, 246,
et seq. (1681.) Crellius, Isagoge, P.
i. L. i. c. 1, p. 3. Alstedius, Eticy-
clop., pp. 29 and 406.
IV. Logica,
Pura,
Applicata,
N.B. — Averroes, (Pacins, Com. p.2),
has Logica ajipropriata sen particida-
ris, and Logica communis =Universal,
Abstract Logic.
V. Logica,
Abstracta,
Concreta.
Pars Commimis,
VI Logica/ { Apodictica, v. Timpler, .S'i/s^. io^r., p. 42. Iseu-
• ^««^*-^'^ P^r^Pro- U.^1^^^.^^^ I doom, Efafa, Cent. i. Eff. 56.
P"^' ( Sophistica,
240
APPENDIX.
EiipeTLKTI Vel TOTTIKT],
Inventio.
VII. LocaCA, ( KpiriKTi.
Jiuliciiiin.
Dispositio.
^v. Timpler, Syd.Log.,-^. 44. Crellius,
Isagoge, pp. 10, 11, and Isendoorn,
Effata, Cent. i. Eff., 51. Adopted
by Agricola, De Inv. Dial., L. i.
p. .35. MelancMiou, Erot. Died.,
J p. 10. Ramus, Schol. Dialect., L.
i. c. i., and L. ii. c. i. p. 351 et
seq. Sjieucer, Log., p. 11. Dow-
n.im, In Rami Dial., L. i. c. 2, p.
14. Perioniiis, De Dialedica, L. i.
J). 6, (1544). Vossius, i)e iV^ai. Arti-
^ um dive Logica, L. iv. c. ix. p. 217.
VIII. Logica,
Pars de Propositio.
Pars de Judicio.
V. Timpler, Sysf. Log., j). 49.
I Doetrina Dividend! . j v. Timpler, S>/st. Log. p. 51. Isen-
IX. Logica, < Doctriua Definiendi. > doom, Effata, Cent. i. Eff., 57.
/ Doetrina Argiimentaudi. \ Boethius, (Aiigustin, Fonseca, &c.)
X. Logica,*
Sunplicis Apprehensi-
onis.
Judicii.
Eatiocinationis.
Noijtica, {melius Noema-
Synthetica. tica.)
Diauoetica.
^
V. Timpler, Syst. Log., 52. Isen-
doorn, Effata, Cent. i. Eff., 58.
\ Isendoorn, Cursus Logicus, p. 31, and
Effata, Cent. i. § 59. Noldius, Log.
Hec, p. 9. Aquinas.
J
XI. Logica,
1. Ideas (notions).
2. Judgment.
3. Peasoning.
4. Method.
UAH de Pemer, Part i. Clericus,
Logica, adopts this division, but
makes Method third. Reasoning
fourth.
XII. Logica,
1. Doctrine of Elements.
2. Doctrine of Method.
Kant, Logik ; Krug, Logik.
1st, Called Analytic by Metz, Inst it. Log. Twesten, Die Logik,
inshesondere die Analytik, p. hi. Esser, Logik. Part i.
2d, Called Systematic or Architectonic by Bachmami, Logik,
Part ii.
Called Synthetic by Esser (who includes xmder it also Applied
Logic), Logik, Part ii.
APPENDIX.
241
XIII. LOGIC-E
IThematica — de materia
operatioui Logicse
siibjecta.
Organica — ■ de iustru-
mentis sciendi.
Mark Dimcan, Instittdiones Logicce,
Proleg. c. iii. § 2, p. 22. Bvirgersdi-
chis, Instit. Log.^ L. i. c. i. p. 5.
/'I. De ordiuibus rerum generalibus
et attribiitis communissimis.
2. De Vocibiis et Oratione.
Commimis ^- ^^ Ideis simplicibus et appre-
Generalis \ bensione simplici dirigenda,
4. De Jiidicio et Propositione.
5. De Discursii.
6. De Dispositione seii Methodo.
XIV. LoGiCA, ( Specialis,
Genetica.
I Genesis stricta.
C Genesis didactica.
(Genesis
sen
Inventio
( Hermenentica.
Analysis | ^nalytica and Critica.
In ordine ad meutem — Logica
stricte dicta.
In ordine ad alios — Interpretativa
vel Hemieueiitica genetica.
I Hermenentica aualytica.
Analytica stricta vel in specie.
Tbeophilus
Gale (Logica,
1681), foUows,
(besides Kec-
kermann and
Bnrgersdyk),
principally
Clauberg and
VArt de Pen-
ser of Port
Royal.
XV. LoGiCxV,
Theoretica pars. ^
Practica pars— (this in- 1 -yyoif^ PMlos. Rationalis, Pars
eluding the Method- / ^^^^ jj_
ology and Applied
Logic of Kant.) j
XVI.
On Adrastean order, &c. of the books of the Organon, vide
Ramus, Scliolce Dial, L ii., c. 8., p. 354. Piccartus, In
' Orgaimm, Prolegomena, p. 1 et seq.
n. riepi T7)9 TrpaJTTjs ivvoias, or
irpoAiitfecos.
XVI.* Logics 1 2. Xlepi (TKi^eus.
partes, \3. nepl /cpitrews.
4. Xlepi ^lavoias.
I 5. Ilepl fi.iQ6Zov.
Eugenins Diaconus, Aoyin)},
p. 144.
VOL. II.
242
APPENDIX.
XVII. LOGICA,
1. Emendatrice.
2. Inventrice.
3. Giudicatrice.
4. Ragionatrice.
5. Ordinatrice.
Genovesi. A division different in some
respects is given in his Latin Logic,
Proleg. § 51, p. 22. The fourth
l)art of the division in the Latin
Logic is omitted in the Italian,
or rather reduced to the second,
and the fifth divided into two.
XV^III. LoGICA,
Vetus,
Nova,
Por2)7iyrii Isag.
Praed. . .
Inter^wet.
Anahjt. Pr.
Analyt. Post
Top. . .
Elench. . .
Isendoorn, Effafa, Cent. i. Eff.
52.
Eeason of terms, Pacius, Com-
ment. in Org., In Porph. Isag.
p. 3.
"XroxewAoyiKri. ,
1 Isendoora, Effata, Cent. i.
XIX. LoGiCA, I ( Apodictica. I Eff. 56. (From John Hos-
•S,v\\oyL(TTiKi). J Topica. pinian, De Controversiis
( Sophistica. Dialedicis.)
XX. LOGICA,
SroixeioAoyiKi';.
Analytica
( Prior.
ca J
Posterior.
I Vossius, De Natura
Artium sive de Lo-
tuWoyiffTiK-i). 1 r • I (/i'^'^f L. iv. C. ix. p.
Dialectica J Topica. I 220.
Sophistica.
XXI. LOGICA,
( prodromus de Interj^retatione.
-Analytica I universe de Syllogism o.
(. speciatim de Demoustratione.
XXII. LoGICA,
ijirodromus de Categoriis.
de Syll. verisimili.
de Syll. sophistico sive pirastico.
Vossiiis, De
) Natura Ar-
tium, p. 220.
\ Dialectica.
^ Analytica.
Aristotle, in Laertius v. Vossius, De
Nat. Art. siveDe Logica, L. iv. c. ix.
§ 11, p. 219.
XXIII. Logica j Rebus quae significantur.l
de \ Vocibus quae significant.]
Stoicorum, see Vossius, De Nat. Art.
sire De Logica, L. iv. c. ix. § 7,
p. 218.
Loquendo.
XXIV. LoGia?i I Eloquendo. (^Varro, vide Vossius, De. Nat. Art.,
partes de ] Proloquendo. / L. iv. c. ix. § 8, p. 219.
Proloquiorum summa.
APPENDIX.
243
XXV. LOGICA,
Logica,
Logicse
partes,
Logicse
partes,
nphs eiipecTiv.
Tlphs Kpiaiv.
Tlphs xpVC"^-
NorjTi/cr;, Apprehensiva.
KpLcri/jLos vel KpiTiK-ij,
Judicativa.
AiaXfKTtK-f], Argiunenta-
tiva.
Divisio.
Defiiiitio.
Argiunentatio.
SApodictica.
Dialectica.
Sophistica.
Logicse ( Analytica.
partes, ( Tojiica.
Aristotle (?) in Laertius, L. v.
§ 28, p. 284. Alexander Aplirod.
in nota Aldobrandini.
Caramiiel Lobkowitz, Eationalis
et Realis PhilosopMa, Logica
sen Phil. Bat. Disp. ii. p. 3.
V. Crellius, Isagoge, Pars, prior, c. i. p. 10.
V. Crellius, Isagoge, Pars, prior, c. i. p. 10.
Isendoorn, Effata, Cent. i. Eff. 54.
> Crellius, Isagoge, Pars, prior, c. i. p. 10.
Stoiclieiology (pure) should contain the doctrine of Syllogism,
without distinction of Deduction or Induction. Deduction, Induc-
tion, Definition, Division, from the laws of thought, should come
under pure Methodology. All are processes, (v. Ceesalpinus,
Qiuest. Perip. sub init.)
Perhaps, 1°, Formal Logic, (from the laws of thought proper),
should be distinguished from, 2°, Abstract Logic, (material, but of
abstract general matter) ; and then, 3°, A Psychological Logic might
be added as a third part, considering how Reasoning, &c., is affected
by the constitution of om^ minds. Applied Logic is properly the
several sciences.
Or may not Induction and Deduction come mider abstract
Material Logic?
244 APPENDIX.
IV.
LAWS OF THOUGHT.
(See Vol. I, p. 84.)
C is either r or uon r
The laws of Identity and Contradiction, each infers the other,
but only through the principle of Excluded Middle ; and the prin-
ciple of Excluded Middle only exists through the supposition of
the two others. Thus, the principles of Identity and Contradiction
cannot move, — cannot be applied, except through supposing the
principle of Excluded Middle ; and this last cannot be conceived,
existent, except through the supposition of the two former. They
are thus co-ordinate but inseparable. Begin with any one, the
other two follow as corollaries.
(a) — Peimary Laws of Thought,— in geneeal.
See the following authors on : — Dreier, Disput. ad Philoso-
phiam Frimam, Disp. v. Aristotle, Analyt. Post. i. c. 11, §§ 2,
3, 4, 5, 6, 7. Schramm, Philosophia Aristotelica, p. 36. Lippius,
Metapyhsica Magna, L. i. c. i., p. 71 et seq. Stahl, Reguloi Philo-
sophicoi, Tit. i., reg. i. p. 2 et seq., reg. ii., p. 8 et seq.. Tit. xix.
reg. viii., p. 520 et seq. Chauvin, Lexicon Philosophicum, v.
Metaphysica. Bisterfeld, evolves all out of ens, — ens est. See
Philosophia Prima, c. ii. p. 24 et seq. Bobrik, System der Logik,
§ 70, p. 247 et seq.
Laws of Thought are of two kinds : — 1°. The laws of the Think-
able, — Identity, Contradiction, &c. 2°. The laws of Thinking in
APPENDIX. 245
a strict sense — viz. laws of ConceptioB, Judgment, and Eeasoning.
See Sclieidler, Psychologie, p. 15, ed. 1833.
That they belong to Logic : — Ramus ScJiol. Dial., L. ix, p. 549.
Is Affirmation or Negation prior in order of thought ? and thus
on order and mutual relation of the Laws among themselves, as
co-ordinate or derived ; (see separate Laws). Fracastorius, Opera,
De Intellectione, L. i. f. 1 25 b., makes negation an act prior to
affirmation ; therefore principle of Contradiction prior to principle
of Identity. — Esser, LogiJc, § 28, p. 57. Sigwart, Handbuch su
Vorlesungen uher die Logik, § 38 et seq. Piccolomineus, Le
Mente Humana, L. iii., c. 4. p. 1301, on question — Is affirmative or
negative prior ? Schulz, Prilf. der Kant. Krit. der reinen Vernunft,
1. p. 78., 2d ed. Weiss, Lehrhuch der Logik, § 81 et seq. pp.
61, 62, 1805. Castillon, Memoires de VAcademie de Berlin
(1803) p. 8, (ContratUction and Identity co-ordinate). A. Andreas,
In Arist. Metaph. iv. Qu. 5, p. 21. (Affirmative prior to nega-
tive.) Leibnitz, CEuvres Philosophiques, Nouv. Ussais, L. iv. ch.
2, § 1, p. 327, ed. Easpe. (Identity prior to Contradiction.) Wolf,
Ontologia, §§55,288 — (Contradiction first. Identity second). Dero-
don, Metaphysica, c. iii., p. 75 et seq. 1669. (Contradiction first.
Excluded Middle second. Identity third). Eonseca, In Metaph.,
I. 849. Biunde, Psychologie, Vol. I, part ii. § 151, p. 159. (That
principle of Contradiction, and principle of Reason and Consequent
not identical, as Wolf and Reimarus hold.) Nic. Taurellus, Philo-
sophic Triumphus, &c., p. 124. Arnheim, 1617. "Cum simplex
ahqua sit affinnatio, negatio non item, banc illam sequi concludi-
mus,'' &c. Chauvin, Lexicon Philosophicum, v. Metaphysica.
By whom introduced into Logic : — Eberstein, {Uher die Bes-
chaffenheit der Logik und Metaphysik der reinen Peripatetiker,
p. 21, Halle, 1800), says that Darjes, in 1737, was the first to in-
troduce Principle of Contradiction into Logic. That Buffier, and
not Reimarus, first introduced principle of Identity into Logic,
see Bobrik, Logik, § 70, p. 249.
(b) — Peimaey Laws of Thought, — in particular.
1. Principle of Identity. " Omne ens est ens." Held good by An-
246 APPENDIX.
tonius Andreas, In Metaph. iv., qu. 5. (apud Fonsecam, In Metaph.
I. p. 849 ; melius apud Suarez, Select. Disp. Metaph. Disp. iii.
sect. iii. n. 4.) Derodon, Metaphysica, c. iii., p. 77. J. Sergeant,
Method to Science, p. 133 — 136 and after. (Splits it absurdly.)
Boethius — " Nulla propositio est verier ilia in qua idem prpedicatur
de seipso." (Versor, In P. Hispani Summulas Logicales, Tr.
vii., p. 441 (1st ed. 1487); et Bmidnnus, Li Sophism.) " Pro-
positiones illas oportet esse notissimas per se in quibus idem de se
ipso prsedicatur, ut ' Homo est homo,' vel quarum prsedicata in
definitionibus subjectarum includuntur, ut 'Homo est animal.'"
Aquinas, Contra Gentiles, L. i. c. 1 0. Opera T. XVIII. p. 7, Venet.
1786. Prior to principle of Contradiction — Leibnitz, Nouveanx
JEssais, p. 377. Buffier, Principes du Raisonnement, 11. art 21, p.
204. Rejected as identical and nugatory by Fonseca, loc. cit.
Suarez, loc. cit. Wolf, Ontologia, §§ ob, 288, calls it Principium
Certitudiuis, and derives it from Principium Contradictionis.
2. Principle of Contradiction — a^tw/xa rrjs az/Tt^acreo)?.
Aristotle, Metaph., L. iii. 3 ; x. 5. (Fonseca, In Metaph. T. I., p.
850, L. iv. (iii.) c. 3.) Anal. Post. L. i. c. 11 c. 2, § 13. (On Aidstotle
and Plato, see Hansel's Prolegomena, pp. 283, 284.) Stahl, Rs-
gulce Philosophicce, Tit. i. reg. i. Suarez, Select Disp. Phil., Disp.
iii. § 8. Timpler, Metaph. L. i., c, 8 qu. 14. Derodon, Meta-
physica, p. 75 etc. Lippius, Metaphysica, L. i. c. i., p. 73. Ber-
nardi, Thes. Aristot., vv. Principium, Cont7^adictio. Leibnitz,
Oeuvres Philosophiques, Nouv. Ess., L. iv. c. 2. Ramus, "Axioma
Contradictionis," Scholce Dial. L. ix. c. i., L. iv. c. 2, § 1, p. 548.
Gul. Xy lander, Institutiones Aphoristicce Logices Aristot, p. 24,
(1577), "Principium principiorum, hoc est, lex Contradictionis."
Philoponus, d^Lcoixa rrjs dvTL(f)da€co<;, v. In Post. An. f. 30 b. et
seq. Ammonius, d^tw/xa Trj<5 dpTL(f)dcre(o<5, In Dc Interpret, f
94, Aid. 1503 ; but principium Exclusi Medii, Scheibler, Topica, c.
19. On Definition of Contradictories, v. Scheibler, Ihid. On Two
Principles of Contradiction, — Negative and Positive, v. Zabarella,
Opera Logica, In An. Post. i. t. 83, p. 807.
Conditions of — Aristotle, Metaph., L. iv., c. 6. Bemardi, The-
saurus Arist., v. Contrad., p. 300.
Proof attempted by — Clauberg, Ontosophia, § 26, (Degerando,
Histoire de Philosophie, T. II. p. 57), through Excluded Middle.
APPENDIX. 247
3. Principle of Excluded Middle — d^toj/xa Stat/oert/coV.
Agicofxa OLaiperiKov, divisivum, dicitur a Grsecis prmci^WM^i
contradictionis afirmativum ; ' Oportet de omni re affirmare aiit
negare,"' Goclenius, Lea^'icon Philosophicum. Lat. p. 136. Zaba-
rella, In. An. Post., L. i., text 83, 02}era Logica, p. 807. Con-
imbricenses, I)i Org., II., 125. Lucian, Opera, II. p. -l-i, (ed.
Hemsterhuis). Aristotle, Metaph., L. iv. (iii.) c. 7 ; An. Post, L. i.
2 ; ii. 13, (Maiisel's Prolegomena, p. 283). Joannes Pliiloponus,
(v. Bernardi, Thes. v. Contrad., p. 300). Piccartus, Isagoge, pp. 290,
291. Javellus, Ln. Metaph., L. iv. qu. 9. Suarez, Disp. Mctaph.,
Disp. iii., sect. 3, § 5. Stahl, RegulcB Philos., Tit. i. reg. 2. Wolf,
Ontologia, §§ 27, 29, 56, 71, 498. Ponseca, In. Metaph., L. iv.
c. iii. qu. 1. et seq., T. I. p. 850. (This principle not first). Tim-
pier, Metaphgsica, L. ii. c. 8, qu. 15. Derodon, Metaph., p. 76
(Secundum principium). Lippius, Metaphysica, L. i. c. i., pp. 72,
75. Chauviu, Lexicon Philosophicum, v. Metaphysica. Scheibler,
Topica, c. 19. Hurtado de Mendoza, Disp. Metaph., Disp. iii., § 3,
(Caramuel, Rat. et Real. Phil, § 452, p. 68).
Whether identical with Principle of Contradiction.
Affirmative, —
Javellus, I. c. Mendoza, Disp. Metaph., D. iii. § 3. Leibnitz,
Oeuvres Philosophiqves, Nouv. Ess., L. iv. c. 2, p. 327.
Negative, —
Fonseca, Disp. Met. Disp. iv. c. 3, 9. Suarez, Disp. Metaph.,
Disp. iii. § 3. Stahl, Reg. Phil. Tit. i. reg. 2.
Whether a valid and legitimate Law.
Pischer, Logik, § 64 et seq. (Negative). — Made first of all prin-
ciples by Alexander de Ales, Metaph., xiv. text 9 : " Conceptus
oranes simplices, ut resolvuntur ad ens, ita omnes conceptus com-
positi resolvuntur ad hoc principium — De quoUhet affirmatio vel
negatio." J. Picus Mirandulanus, (after Aristotle), Gonclusiones,
Opera, p. 90. Philoponus, In An Post. i. f 9 b, (Brandis,
Scholia, p. 199.) To 8' airau (ftdpai rj aTTOfj^dvai, r) ets to
248 APPENDIX.
aS-uvaTov aTToSet^t? Xafx/Savei. Aristotle, An. Post. i. c. 11. § 8.
'AvTL(f)aai'^ Se avTiBecri'? rjs ovk ean fxera^v KaO" avTTjV.
An. Post. i. c. 2, § 13. Mera^u di^rt^acreoj? ovk ez^Se^erat
ovOiv. Metaph. L. iii. c. 7. 'EttcI dvTLcjidcrea)? ovSev dvd
jxeaov, (fyavepov on iv To1<i evavrioi<^ eVrat to [xera^v.
Physica, L. v. c. 3, § 5. See also Pos^. An. L. i. c. i. § 4, p. 414 ;
c. 2, § 13, p. 417; c. 11. § 3, p. 440, (vide Scheibler, Topica,
c. 19 ; and Mansers Prolegomena, p. 283, on Aristotle.)
4 Principle of Eeason and Consequent.
That can be deduced from Principle of Contradiction.
Wolf, Otitologia, § 70. Baumgarten, Metaphysik, § 18.
Jakob, Grundriss der allgemeinen Logik und Kritische Ang-
fangsgrilnde der allgemeinen Metaphysik, p. 38, 3d ed., 1794.
(See Kiesewetter, I. c.)
That not to be deduced from Principle of Contradiction.
Kiesewetter, Allgemeine Logik ; Weitere Auseinandersetzung,
P. I. ad §§ 20, 21, p. 57 et seq. Hume, On Human Nature, Book
i. part. iii. § 8. Schulze, Logik, § 18, 5th ed., 1831.
APPENDIX. 249
V.
NEW ANALYTIC OF LOGICAL FOEMS— GENEEAL
EESULTS— FEAGMENTS.
(a) Extract from Prospectus of " Essay towards a New
Analytic of Logical Forms."
(First publislied in 1846." See above, Vol. I, pp. 144, 244.— Ed.)
" Now, wJuit has been the source of all these evils, I 'proceed to relate, and shall clearly
convince those tvho have an intellect and a will to attend, — that a trivial slip in the ele-
mentari/ j^recepts of a Logical Theory, becomes the cause of mightiest errors in that Theory
itself." — Galen. {De Temperamentis, 1. i. c. 5.)
" This New Analytic is intended to complete and simplify the
old ; — to place the keystone in the Aristotelic arch. Of Abstract
Logic, the theory, in particular of Syllogism, (bating some improve-
ments, and some errors of detail), remains where it was left by the
genius of the Stagirite ; if it have not receded, still less has it ad-
vanced. It contains the truth ; but the truth, partially, and not
always correctly, developed, — in complexity, — even in confusion.
And why ? Because Aiistotle, by an oversight, marvellous certamly
in him, was prematurely arrested in his analysis ; began his syn-
thesis before he had fully sifted the elements to be recomposed ;
and, thus, the system which, abnost spontaneously, would have
evolved itself into unity and order, he laboriously, and yet imper-
fectly, constructed by sheer intellectual force, under a load of limi-
tations and corrections and rules, which, deforming the symmetry,
a An extract correspouding in part (in the Edinburgh Review) first published
with that now given from the Prospectus in 1833, the theory of Induction there
of "Essay towards a New Analytic of maintained proceeds on a thorough
Logical Forms," is republished in the -Dzs- quantification of the predicate, in aflSr-
cussions on Philosophy, p. 650. To this mative propositions,
extract the Author has prefixed the fol- Before 1840, I had, however, become
lowing notice regarding the date of his convinced that it was necessary to ex-
doctrine of the Quantification of the Pre- tend the principle equally to negatives ;
dicate : — " Touching the principle of an for I find, by academical documents,
explicitly Quantified Predicate, I had, by that in that year, at latest, I had pub-
1833, become convinced of the necessity licly taught the unexclusive doctrine."
to extend and correct the logical doctrine — Discussions, p. 650. — Ed.
upon this point. In the article on Logic
250 APPENDIX.
has seriously impeded the usefulness, of the science. This imper-
fection, as I said, it is the purpose of the New Analytic to supply,
" In the first place, in the Essay there will be shown, that the
Syllogism proceeds, not as has hitherto, virtually at least, been
taught, in one, but in the two correlative and counter wholes
(Metaphysical) of Comprehension, and (Logical) of Extension ;
the major premise in the one whole, being the minor premise in
in the other, &c. — Thus is relieved, a radical defect and vital in-
consistency in the present logical system.
" In the second place, the self-evident truth, — That we can only
rationally deal with what we already understand, determines the
simple logical postulate, — To state explicitly ivhat is thought ira-
plicitly. From the consistent application of this postulate, on
which Logic ever insists, but which Logicians have never fairly
obeyed, it follows : — that, logically, we ought to take into account
the quantity, always understood in thought, but usually, and for
manifest reasons, elided in its expression, not only of the subject,
but also of the predicate, of a judgment. This being done, and
the necessity of doing it will be proved against Aristotle and his
rejieaters, we obtain inter alia, the ensuing results : —
"1°. Thdii t\iQ 2^'f'^i^dcsignate terms oi a proposition, whether
subject or predicate, are never, on that account, thought as indefi-
nite (or indeterminate) in quantity. The only indefinite, is parti-
cular, as opposed to definite, quantity ; and this last, as it is either
of an extensive maximum undivided, or of an extensive minimum
indivisible, constitutes quantity universal, (general), and quantity
singular, (individual). In fact, definite and indefinite aie the only
quantities of which we ought to hear in Logic ; for it is only as
indefinite that particular, it is only as definite that individual and
general, quantities have any (and the same) logical avail.
" 2°. The revocation of the two Terms of a proposition to their
true 7'elation ; a proposition being always an equation of its sub-
ject and its predicate.
" 3°. The consequent reduction of the Conversion of Propositions
from three species to one, — that of Simple Conversion.
" 4°. The reduction of all the General Laws of Categorical Syllo-
gisms to a Single Canon.
" 5°. The evolution from that one canon of all the Species and
varieties of Syllogism.
APPENDIX. 251
" 6°. The abrogation of all the Special Laws of Syllogism.
" 7°. A demonstration of the exclusive possibility of Three syllo-
gistic Figures ; and (on new grounds) the scientific and final abo-
ition of the Fourth.
" 8°. A manifestation tha,tFigure is an unessential variation in
syllogistic form ; and the consequent absurdity of Reducing the
syllogisms of the other figures to the first.
" 9°. An enouncement oi one Organic Principle iov each Figure.
" 10°. A determination of the true number of the legitimate
Moods ; with
" 11°. Their amplification in number (thirty-six) ;
u 22°. Their numerical equality under all the figures ; and,
" J 3°. Their relative equivalence, or virtual identity, throughout
every schematic difference.
"14°. That, in the second and third figures, the extremes holding
both the same relation to the middle term, there is not, as in the
first, an opposition and subordination betiueen a term major and
a term minor, mutually containing and contained^ in the counter
ivholes of Extension and Comprehension.
" 15°. Consequently, in the second and third figures, there is no
determinate major and minor premise, and there are two indiffe-
rent conclusions ; whereas, in the first the premises are determi-
nate, and there is a single proximate conclusion.
" 1 6°. That the thi7^d, as the figure in which Comprehension is
predominant, is more appropriate to Induction.
"17°. That the second, as the figure in which Extension is pre-
dominant, is more appropriate to Deduction.
" 18°. That i\\Q first, as the figure in which. Comprehension and
Extension are in equilibrium, is common to Induction and Deduc-
tion, indifferently.
" In the third place, a scheme of Symbolical Notation will be
given, wholly different in principle and perfection from those
which have been previously proposed ; and showing out, in all
their old and new applications, the propositional and syllogistic
forms, with even a mechanical simplicity.
" This Essay falls naturally into two parts. There will be con-
tained, — in the first, a systematic exposition of the new doctrine
itself ; in the second, an historical notice of any occasional antici-
252 APPENDIX.
pations of its several parts whicli break out in the writings of pre-
vious philosophers.
" Thus, on the new theory, many valid forms of judgment and
reasoning, in ordinary use, but which the ancient logic continued
to ignore, are now openly recognised as legitimate ; and many
relations, which heretofore lay hid, now come forward into the
light. On the one hand, therefore. Logic certainly becomes more
complex. But on the other, this increased complexity proves only
to be a higher development. The developed Syllogism is, in effect,
recalled, from multitude and confusion, to order and system. Its
laws, erewhile many, are now few, — we might say one alone, — but
thoroughgoing. The exceptions, formerly so perplexing, have
fallen away ; and the once formidable array of limitary rules has
vanished. The science now shines out in the true character of
beauty, — as One at once and Various. Logic thus accomplishes
its final destination ; for as ' Thrice-greatest Hermes,' speaking in
the mind of Plato, has expressed it, — ' The end of Philosophy is
the intuition of Unity.' "
(6) — Logic, — Its Postulates.
(November 1848— See above, Vol. L, p. 114.)
I. To state explicitly what is thought implicitly. In other
words, to determine what is meant before proceeding to deal with
the meaning. Thus in the proposition Me7i are animals, we
should be allowed to determine whether the term men means all
or some men, — whether the term animals means all or some ani-
mals ; in short, to quantify both the subject and predicate of the
proposition. This postulate applies both to Propositions and to
Syllogisms.a
a See (quoted by Wallis, Lorjica, argiimentationis consequentia propter
p. 291) Aristotle, An. Prior., L. i., c. crypsin] dubitatio fuerit, explenda qua3
33 (PaciiTS, c. 32, §§ 2, 3, 4, p. 261), desuut ; amputanda quee supersunt ; et
and Ramus, (from Downam, In P. pars quselibet in locum redigenda situ
Rami Dialect., L. ii., c. 9, p. 410) : est." [Cf. Ploucquet, Elementa Philo-
What is understood to be supplied ; sophlm Contemplativcc, § 29, p. 5. Stut-
[^Ranuis Dial., L. ii., c. 9. " Si qua [de gardise, 1778. " Secundum sensum lo-
APPENDIX. 253
II. Throughout the same Proposition, or Immediate (not me-
diate) Reasoning, to use the same words, and combinations of words,
to express the same thought a, (that is, in the same Extension and
Comprehension), and thus identity to be presumed.
Thus a particular in one (prejacent) proposition of an immediate
reasoning, though indefinite, should denote the same paH in the
other. This postulate applies to inference immediate, e. g. Con-
version.
Predesignate in same logical unity, ([proposition or syllogism),
in same sense, both Collective or both Distributive. That one
term of a proposition or syllogism should not be used distributively
and another collectively.
III. And, e contra, throughout the same logical unity, (immediate
reasoning), to denote and presume denoted the same sense (notion or
judgment) by the same term or terms./^
This does not apply to the different propositions of a Mediate
Inference.
IV. (or V.) To leave, if necessary, the thought undetermined, as
subjectively uncertain, but to deal with it only as far as certain or
determinable. Thus a whole may be truly predicable, though we
know only the truth of it as a part. Therefore, we ouglit to be
able to say some at least when we do not know, and cannot, there-
fore, say determinately, either that some only or that all is true.
(January 1850.)
III. (or IV.) To be allowed, in an immediate reasoning, to de-
gicum ct;m omni termino jungendum cal proposition, If the Chinese are Ma-
est signum quantitatis." — Ed.] liometans, they are {some} infidels ; the
a Tliat words must be used in the word infidel, unless thought in a mean-
same sense. See Aristotle, Anal. Pr., ing limited to and true of Mahometans,
L. i., cc. 33, 34, 35, 36, 37, &c. is inept. But if it be so limited, we
/3 If these postidates (II. and III.) can (contrary to the doctrines of the
were not cogent, we could not convert, logicians) argue back from the position
at least not use the converted proposi- of the consequent to the position of the
tion, (unless the I, were cogent, the con- antecedent, and from the sublation of
vertenda would be false). All man is the antecedent to the sublation of the
(an) animal, is converted into iSome consequent, though false. If not gi-anted,
animal is {all) man. But if the some Logic is a mei'e childish play with the
animal here were not thought in and vagueness and ambiguities of language
limited to the sense of the convertend, [Cf. Titius, Ars Gorjitandi, c. xii., § 26. —
it would be false. So in the Hypotheti- Ed.]
254 APPENDIX.
note, that another part, other, or some, is used in the condusion,
from what was in the antecedent. Inference of Sub-contrariety.
That the some, if not otherwise qualified, means some only, —
this by presumption.
That the Term (Subject, or Predicate) of a Proposition shall be
converted with its quantity unchanged, i. e. in the same extension.
This violated, and violation cause of error, and confusion, ^oper
accidens, for the real terms compared are the quantified terms,
and we convert only the terms compared in the prejacent or con-
vertenda.
That the same terms, apart from the quantity, i. e. in the same
comprehension, should be converted. As before stated, such terms
are new and different. No Contraposition, for contraposition is only
true in some cases, and even in these it is true accidentally, not by
conversion, but through contradiction ; i. e. same Comprehension.
That we may see the truth from the necessary validity of the
logical process, and not infer the validity of the logical process
from its accidental truth. Conversion j;e?' accidens, and Contra-
position, being thus accidentally true in some cases only, are logi-
cally inept, as not true in all.
To translate out of the complexity, redundance, deficiency, of
common language into logical simplicity, precision, and integrity."
(December 1849).
As Logic considers the form and not the matter, but as the form
is only manifested in application to some matter, Logic postulates
to employ any matter in its examples.
(January 1850).
That we may be allowed to translate into logical language the
rhetorical expressions of ordinary speech. Thus the Exceptive and
Limitative propositions in which the predicate and subject are pre-
designated, are to be rendered into logical simplicity.
a See above, p. 252, note o. — Ed.
APPENDIX. 255
(May 1850).
As Logic is a formal science, and professes to demonstrate by-
abstract formulfe, we should know, therefore, nothing of the no-
tions and their relations exce23t ex facie of the propositions. This
implies the necessity of overtly quantifying the predicate.
(c) — Quantification of Predicate, — Immediate
Inference, — Conversion, — Opposition."
(See above, Vol. I., pp. 244, 262.)
We now proceed to what has been usually treated under the
relation of Propositions, and previously to the matter of Infer-
ence altogether ; but which I think it would be more correct to
consider as a species of Inference, or Eeasoning, or Argumenta-
tion, than as merely a preparatory doctrine. For in so far as these
relations of Propositions warrant us, one being given, to educe
from it another, — this is manifestly an inference or reasoning.
Why it has not always been considered in this light, is evident.
The inference is immediate ; that is, the conclusion or second pro-
position is necessitated directly and without a medium, by the first.
There are only two propositions and two notions in this species of
argumentation ; and the logicians have in general limited reason-
ing or inference to a mediate eduction of one proposition out of
the correlation of two others, and have thus always supposed the
necessity of three terms or collated notions.
But they have not only been, with few exceptions, unsystematic
in their procedure, they have all of them, (if I am not myself
mistaken), been fundamentally erroneous in their relative doctrine
There are various Immediate Inferences of one proposition from
another. Of these some have been wholly overlooked by the lo-
gicians ; whilst what they teach in regard to those which they do
consider, appears to me at variance with the truth.
I shall make no previous enumeration of all the possible species
« Appendix (c),from p. 255 to p. 274, of Conversion as given above, vol. i., p.
was usually delivered by the author as a 262. — Ed.
Lecture, supplementary to the doctrine
256 APPENDIX.
of Immediate Inference ; but shall take them up in this order : —
I shall consider, 1°, Those which have been considered by the logi-
cians; and, 2°, Those which have not. And in treating of the
first group, I shall preface what I think the true doctrine by a
view of that whicli you will find in logical books.
The first of these is Conversion. When, in a categorical propo-
sition, (for to this we now limit our consideration), the Subject and
Predicate are transposed, that is, the notion which was previously
the subject becomes the predicate, and the notion which v/as pre-
viously the predicate becomes the subject, the proposition is said
to be converted." The projDosition given, and its product, are to-
gether called the judicia conversa, or propositiooies converses,
whicli I shall not attemj)t to render into English. The relation
itself in which the two judgments stand, is called conversion, re-
ciprocation, transposition, and sometimes obversion, (conversio,
recip>rocatio, transpositio, ohversio.)
The original or given proposition is called the Converse, or
Converted, sometimes the Prcejacent, Judgment, {judicium, or
propositio, conversum, conversa, prcejacens) ; the other, that into
which the first is converted, is called the Converting, and some-
times the Subjacent, Judgement, {propositio, or jud. convertens,
subjacens). It would be better to call the former the Convertend,
{p)r. convertenda), the latter the Converse, {yr. conversa). This
lauouao-e I shall use.'^
a [Definitions of conversion in general. [Names for the two propositions in
'ApTiaTpo(j)r] iffTiv t(TO(rTpo(pr] ris, Phil- Conversion.
oponus, (or Ammonius); In An. Pr., i. I. Name for the two coiTelative j^ro-
c. 2, f. lib. So Magentinus, /?i 4 m.. Pr. positions — Conversa, Twesteu, ioy«X-, §
i. c. 2, f. 3 b. Anonymus, De Syllo- 87, Contraposita, /(/. ibid,
gismo, f. 42 b. UpoTaa-ecos avTi.(rrpo(p7} II. Original, or Given Proposition.
ecTTi KOLvwvia 5to TTpoTaffiwv Kara rovs a) 7] Trpo7]yovfj.evr], irpo/cei/xeVrj, avTiarpe-
'6povs a,vdira\iv ridefj-evovs, fieTO, rov (Tvv- (poixevri TrpSraais — Cf. Strigelius, In
a\r]Bfveiv. Alexander, /;; An. Pr. i. c. 4, Miianchth. Erot. Dial., L. ii., p. 581.
f . 15 b. See the same in different words, 'AvTia-rpfipovaai irporaffeis, Philopon-
by Philoponus, (Ammouius), In An. Pr., \is, (quoted by Wegelin, /. c.)
i. c. 2, f. 11 b., and copied from him by b) Conversa (= Convertenda) vulgo.
Magentinus, In An. Pr., f. 3 b. Cf. Scotus, Qucvstmies in An. Prior., i.
Boethius, Opera, Introductio ad Syllo- q. 12. Corvinus, Instit. Phil., § 510.
gismos, p. 574. Wegelin, in Gregorii Richter, Be Conversione, 1740. Halso
Aneponymi Phil. Syntag. (circa 1260), Magdeb. Baumgarten, Logica, § 278.
L. v., c. 12. p. 621. Nicephorus Blem- 1J\vich.,In»tit.Log. e<Jfe<.,§182,p. 188.
midas, Epit. Log., c. 31, p. 221.] c) Convertibilis (rare).
^ See above, vol. i., p. 262. — Ed. d) Convertens, Micraelius, Lex. Phil. v.
APPENDIX. 257
Such is the doctrine touching Conversion, taught even to the
present day. This in my view is beset with errors ; but all these
errors originate in two, as these two are either the cause or the
occasion of every other.
The First cardinal error is, — That the quantities are not con-
verted with the quantified terms. For the real terms compared in
the Convertend, and which, of course, ought to reappear without
change, except of place, in the Converse, are not the naked, but the
quantified terms. This is evident from the following considerations :
J °, The Terms of a Proposition are only terms as they are terms
of relation ; and the relation here is the relation of comparison.
2°, As the Prepositional Terms are terms of comparison, so they
are only compared as Quantities, — quantities relative to each other.
An Aflirmative Proposition is simply the declaration of an equation,
a Negative Proposition is simply the declaration of a non-equation,
of its terms. To change, therefore, the cpiantity of either, or of
both Subject and Predicate, is to change their correlation, — the
point of comparison ; and to exchange their quantities, if different,
would be to invert the terminal interdependence, that is, to make
the less the greater, and the greater the less.
3°, The Quantity of the Proposition in Conversion remains always
the same ; that is, the absolute quantity of the Converse must be
exactly equal to that of the Convertend. It was only from over-
looking the quantity of the predicate, (the second error to which we
Converslo. Twesten, Lof/il\, § 87. An- a) t] avna-rpffova-a. See Strigelius, loc.
tecedens, Scotus, I. r. Strigelius, /. c. cit.
e) PiU'jacens, Scheibler, Opera Lor/ira, h) Convertens, Subjacens, Scotus, Quws-
I)e Propositionihus, Pars. iii. c. x. p. tiones, In An. Prior, i. 9, 24, f. 276,
479. et passim. Krug, Lur/il; § 65, p. 205,
f) Exposita, Akb'ich, Comp., L. i. c. 2. and logicians in general.
Whately, Zor/t'c, p. 69. Propositio ex- c) Conversa, Boethius, Opera, In trod.
posita, or exponens, quite different as ad Si/ll., -pp. 575 ef seq., 587 et scq.;
used by Logicians, v. Scliegkius, /// Melanchthon, Z;>o<e»iate, L. ii. jd. 681,
Arist. Orcj. 162 (and above, vol. i., p. and Strigelius, ad lor. Micraelius,
263.) leoc. Pfiil., 7\ Conrersio. Noldius,
g) Convertenda, Corvinus, loc. cit. Rich- Logica Recognita, p. 263, says that
ter, loc. cit. the first should more probablj^ be
h) Contraponens, Twesten, Ihid. called Convertibilis, or Convei-tenda,
i) Prior, Boethius, De Syllog. Categ. L. and the second Conversa.
I. 0/Jera, p. 588. d) Conversum, Twesten, loc. cit.
k) Principium, Darjes, Via ad Verita- e) Contrapositum, Id. ihid.
tern, § 234. f) Conclusio, Darjes, Via ad Veritatcm,
III. Product of Conversion. § 234.
VOL. II. R
258 APPENDIX.
sTiall immediately advert), that two propositions, exactly equal in
quantity, in fact the same proposition, perhaps, transposed, were
called the one universal, the other jmrticulm', by exclusive refer-
ence to the quantity of the subject.
4°, Yet was it of no consequence, in a logical point of view,
which of the notions collated were Subject or Predicate ; and their
comparison, with the consequent declaration of their mutual incon-
clusion or exclusion, that is, of affirmation or negation, of no more
real difference than the assertions, — London is four hundred
miles distant from Edinburgh, — Edinburgh is four hundred
miles distant from London. In fact, though logicians have
been in use to place the subject first, the predicate last, in their
examples of propositions, this is by no means the case in ordinary
language, where, indeed, it is frequently even difficult to ascertain
which is the determining and which the determined notion. Out
of logical books, the predicate is found almost as frequently before
as after the subject, and this in all languages. You recollect the
first words of the First Olyminad of Pindar, ''ApicTTOv ixev vSop,
"Best is water ;" and the Vulgate, (I forget how it is rendered in
our English translation), has, "Magna est Veritas, et prsevalebit." «
Alluding to the Bible, let us turn up any Concordance under any
adjective title, and we shall obtain abundant proof of the fact. As
the adjective great, magnus, has last occurred, let us refer to
Cruden under that simple title. Here, in glancing it over, I find —
" Great is the wrath of the Lord — Great is the Lord and greatly to be
praised — Great is our God — Great are thy works — Great is the Holy
One of Israel — Great shall be the peace of thy children — Great is thy
faithfulness — Great is Diana of the Ephesians — Great is my boldness
— Great is my glorying — Great is the mystery of godliness," &c.
The line of Juvenal,
"Nobilitas sola est atqne imica virtus,"
is a good instance of the predicate being placed first.
The Second cardinal error of the logicians is, the not considering
that the Predicate has always a quantity in thought, as much as
the Subject ; although this quantity be frequently not explicitly
enounced, as unnecessary in the common emijloyment of language ;
a III. Esdras iv. 41 : " Magna est veri- (I. Esdras iv. 41), " Great is truth, and
tas et prsevalet." In the English version, mighty above all things." — Ed.
APPENDIX. 259
for tlie determining notion or predicate being always thought as at
least adequate to, or co-extensive with, the subject or determined
notion, it is seldom necessary to express this, and language tends
ever to elide what may safely be omitted. But this necessity
recurs, the moment that, by conversion, the predicate becomes the
subject of the proposition ; and to omit its formal statement is to
degrade Logic from the science of the necessities of thought, to an
idle subsidiary of the ambiguities of speech. An unbiassed con-
sideration of the subject will, I am confident, convince you that
this view is correct,
1°, That the jjredicate is as extensive as the subject is easily
shown. Take the proposition, — All animal is man, or, All ani-
mals are men. This we are conscious is absurd, though we make
the notion man or men as wide as possible ; for it does not mend
the matter to say, — All animal is all man, or. All animals are
all men. We feel it to be equally absurd as if we said, — All man
is all animal, or. All men are all animals. Here we are aware
that the subject and predicate cannot be made coextensive. If we
would get rid of the absurdity, we must bring the two notions into
coextension, by restricting the wider. If we say — Man is animal,
{Homo est animal), we think, though we do not overtly enounce
it, All man is animal. And what do we mean here by animal ?
We do not think, — All, but Some, animal. And then we can
make this indifferently either subject or predicate. We can think,
— we can say. Some animal is man, that is, Seine or All Man ;
and, e converso, — Man (some or all) is animal, viz. so7ne animal.
It thus appears that there is a necessity in all cases for thinking
the predicate, at least, as extensive as the subject. Whether it be
absolutely, that is, out of relation, more extensive, is generally of
no consequence ; and hence the common reticence of common
language, which never expresses more than can be understood, —
which always, in fact, for the sake of brevity, strains at ellipsis.
2°, But, in fact, ordinary language quantifies the Predicate so
often as this determination becomes of the smallest import. This
it does either directly, by adding all, some, or their equivalent pre-
designations, to the predicate ; or it accomplishes the same end
indirectly, in an exceptive or limitative form.
a) Directly, — as Peter, John, James, &c., are all the Apostles
— Mercury, Venus, &c., are all the planets.
260
APPENDIX.
b) But this is niore frequently accomplished indirectly, by the
equipollent forms of Limitation or Inclusion, and Exception. «
For example, by the limitative designations, alone or only, we
say, — God alone is good, which is equivalent to saying, — God is all
good, that is, God is all that is good ; Virtue is the only nobi-
lity, that is. Virtue is all nohle, that is, all that is nohlefi The
symbols of the Catholic and Protestant divisions of Christian-
ity may afford us a logical illustration of the jioint. The Ca-
tholics say, — Faith, Hope, and Charity alone justify ; that is, the
three heavenly virtues together are all justifying, that is, all that
justifies; omne justificans, justum faciens. The Protestants
say, — Faith alone justifies ; that is, Faith, which they hold to
comprise the other two virtues, is all justifying, that is, all that
a By the logicians this is called simply
Exclusion, and the particles, tantum, &c.,
particuke exclasivce. This, I think, is
inaccurate ; for it is inclusion, limited by
an exclusion, that is meant. — [See Schei-
bler, Opera Logica, P. iii., c. vii., tit. 3,
p. 457 et seq.]
i8 (February 1850.) On the Indirect
Predesignation of the Predicate by what
are called the Exclusive and Exceptive
praficles.
Names of the particles.
Latin, — iimis, unicus, unice ; solus,
solum, solummodo, tantum, tantummodo ;
duntaxat ; prcecise ; ad(equate. Nihil
prceter, — prwterquam, — ni nisi non.
English, — one, 07ily, alone, exclusively,
precisely, just, sole, solely, nothing but,
not except, not beyond.
I. These particles annexed to the Sub-
ject predesignate the Predicate univer-
sally, or to its whole extent, denying its
particularity or indefinitude, and defi-
nitely limiting it to the subject alone.
As, Man alonephilosophhes, (though not
all do). The dog alone barks, or, dogs
alone bark, (though some do not). Man
only is rational, or No animal but man is
rational. Nothing but rational is risible.
Of material things there is iwthing living
(but) not organised, and nothing organ-
ised not living. God alone is to be wor-
shipped. God is the single, — sole object
of worship. 'Some men only are elect.
II. Annexed to the Predicate, they
limit the subject to the predicate, but
do not define its quantity, or exclude
from it other subjects. As, Peter only
plays. The sacraments are only tivo.
The categories are only ten. John drinks
only loater.
III. Sometimes the particles eole,
solely, single, alone, only, &c., are an-
nexed to the Predicate as a predesigna-
tion tantamount to all. As, God is the
single, — one, — alone, — only, — exclusive,
— adequate, object of worship.
On the relation of Exclusive proposi-
tions to those in which the predicate is
predesignated, see Titius, Ars Cogitandi,
c. vi. §§ QQ, 67. Hollman, Philosophia
Bationalls, § 475. Kreil, Handbuch der
Logik, § 62. Derodon, Logica Restituta,
De Enunciatione, c. v. p. 569 et seq.
Keckerman, Systema Logicce, lib. iii., c.
11. Opera, t. i. p. 763.
The doctrine held by the logicians as
to the exclusum prcedicatum, exchisum
subjectum, and exclusum signum, is er-
roneous. — See Scheibler, Opera Logica,
P. iii., c. vii., tit. 3, p. 457 et seq. Jac.
Thomasius, Erotem. Log., c. xxx. p. 67 et
seq. [Cf. Fonseca, Instit. Dial., L. III.
c. 23. For a detailed exposition of this
doctrine by Scheibler, see below, p. 261,
note o. — Ed.]
APPENDIX.
261
justifies ; omne justificans. In either case, if we translate the
watchwords into logical simplicity, the predicate appears prede-
signated.
Of animals man alone is rational ; that is, Man is all rational
animal. What is rational is alone or only risible ; that is, All
rational is all risible, &c.
I now pass on to the Exceptive Form. To take the motto over-
head, — " On earth there is nothing great but man." What does
this mean ? It means, Man — is — all earthly great. — Homo — est
— omne magnum terestre. And the second clause — "In man
there is nothing great but mind," — in like manner gives as its
logical equipollent — Mind — is — all humanly great, that is, all that
is great in man. {Mens est omne magnum humanum.)a
We ought, indeed, as a corollary of the postulate already stated,
to require to be allowed to translate into equivalent logical terms
a Vide Scheibler, Opera Logica, P. iii.
c. vii. pp. 458, 460, where his examples,
with the exposition of the Logician.?,
may be well contrasted with mine.
[Scheibler, after referring to the
Parva Logicalia of the schoolmen, a.s
containing a proposed supplement of
the doctrines of Aristotle, pi-oceeds to
exjjound the Propositiones Exponihiles
of those treatises. " Exclusiva enun-
ciatio est, qua; habet particulam ex-
clusivam, ut. Solus homo est rationahs.
Pori'o exclusivaj ennn-
ciationes sunt duplicis generis. Alise
sunt exclusivse prsedicati : alife exclu-
sivae subjecti ; hoc est, in aliis parti-
cula exclusiva excludit a subjecto, in
aliis excludit a prgedicato, veluti ha3c
propositio exclusiva est : Deus tantum
est iminortalis . Estque exclusiva a sub-
jecto, hoc sensu, Deus tantum, et non
homo vel lapis, &c Omnes
propositiones exclusiva; ambiguo; sunt,
si habeaut particulam exclusivam, post
subjectum propositionis, ante vinculum,
ut erat in proposito exemplo. Carent
autem propositiones exclusivse ilia am-
biguitate, si vel exclusiva particula, pon-
atur ante subjectum propositionis, vel
etiam sequatur copulam. Ibi enim
indicatur esse propositio exclusiva sub-
jecti, ut, solus homo discurrit. Hie au-
tem indicatur, esse propositio exclusiva
prtcdicati, ut, Sacramenta Novi Testa-
meiiti sunt tantum duo. Pnedicamenta
tantmn decern."
Scheibler then proceeds to give the
following general and special rules of
Exclusion : —
" I. Generaliter tenendum est, quod
allter sint exponendce exclusivce a prcedi-
cato, et aliter exclusivce a subjecto.
" II. Exclusiva propositio non excludit
concomitantia.
"III. Omnis exclusiva resolvitur induas
simplices, altefam affirmatam, alteram
negatam. Atque hoc est quod vulgo
dicitur, quod omnis exclusiva sit hypo-
thetica. Hypothetica enim projjositio
est qua3 includit duas alias in virtute,
vel disi^ositioue sua. Veluti hsec, Solus
homo est rationalis, aequivalet his dua-
bus, Homo est rationalis, et q^iod non est
homo, non est rationale. Et in specie,
Bestia non est rationalis. Planta non
est rationalis Atque
hse dua; propositiones vocantur expon-
entes, sicut propositio exclusiva dicitur
exjMnibilis.
" Speciales autem regulae explicandi
exclusivas sunt octo: sicut et octo sunt
genei'a locutionum exclusivarum.
262
APPENDIX.
tlie rhetorical enouncements of common speech. We should not
do as the logicians have been wont, — introduce and deal with these
in their grammatical integrity; for this would be to swell out and
deform our science witli mere grammatical accidents ; and to such
fortuitous accrescences the formidable volume, especially of the
older Logics, is mainly owing. In fact, a large proportion of the
scholastic system is merely grammatical.
3°, The whole doctrine of the non-quantification of the predicate
is only another example of the passive sequacity of the logicians.
They follow obediently in the footsteps of their great master. We
owe this doctrine and its prevalence to the precept and authority
of Aristotle. He prohibits once and again the annexation of the
universal predesignation to the predicate. For why, he says, such
predesignation would render the proposition absurd ; giving as his
only example and proof of this, the judgment — All man is all
animal. This, however, is only valid as a refutation of the ridicu-
lous doctrine, held by no one, that any predicate may be universally
"I. Proposltio exclusiva universalis af-
Jirmativa, cujus si[/num non ner/atur, ut,
Tantum omnis homo cuiYit, exponitur
sic, Omnis homo currit, et nihil aliud ab
homine currit. Vocari solet ha3C exposi-
tio Pater, quia prior ejus pars est uni-
versalis afRrmativa, quod notat A. Et,
alterse pars est universalis negativa, quod
indicat in posteriori syllaba litera E.
" II. Propositio particvlaris, vel inde-
finita affirmativa, in qua signum non
negatur, ut Tantum homo currit, exponi-
tur sic, Uomo currit, et nihil aliud ab
homine currit. Vocatur hsec expositio,
NiSE.
" III. Propositio exclusira, in qua sig-
num non negatur, universalis negativa, ut,
Tantum nullus homo curnt, exponitur sic,
Nullus homo currit, et quodlibet aliud ab
homine currit, vocatur, Tenax."
" IV. Exclusiva cujus signum non ne-
gatur particular is vel indefinita negativa,
ut, Tantum homo non currit, exponitur
sic, Homo non currit, et quodlibet aliud
ab homine currit, vocatur, Storax.
"V. Exclusiva, in qua signum negatur,
affirmativa et universalis, ut, Non tan-
tum omnis homo currit, exponitur sic,
Omnis homo cuirit, et aliquod aliud ab
homme currit, vocatur, Canos.
" VI. In qua signum negatur, existens
universalis affirmativa, ut, Non tantum
nullus homo currit, sic exponitur, Nidlus
homo currit, et aliquid aliud ab homine
non currit, vocatur. Fecit.
" VII. Exclusiva, in qua signum nega-
tur, existens particularis affirmativa, ut,
Non tantum aliquis homo currit, expositur
sic, Aliquis homo currit, aliquid aliud
ab homine currit, vocatur, Pilos,
" VIII. Negativa particularis exclu-
sive propositiones, cujus signum negatur,
ut, Non tantum aliquis homo non currit,
exponitur sic, A liquis homo non currit, et
aliquid aliud ab homine non cwTit,yoca-
tur. Nobis.
" Differentia autem propositionis ex-
clusiva3 et exceptivue est evideus. Nempe
exclusiva prajdicatum vendicat uni sub-
jecto, aut asubjecto excludit alia prajdi-
cata, ut, S'ulus Dcus bonus est. Exceptiva
avitem statuit universale subjectum, in-
dicatque aliquid contiueri sub isto uni-
versali, de quo non dicatur prtcdicatum,
ut, Onme animal est irrationale, i:)rwtcr
hominem." — Ed.]
APPENDIX. 2G3
quantified ; for, to employ his own example, what absurdity is
there in saying that some animal is all man ? Yet this non-
sense, (be it spoken with all reverence of the Stagirite), has imposed
the precept on the systems of Logic down to the present day.
Nevertheless, it could be shown by a cloud of instances from the
Aristotelic writings themselves, that this rule is invalid ; nay
Aristotle's own doctrine of Induction, which is far more correct
than that usually taught, proceeds upon the silent abolition of the
erroneous canon. Tlie doctrine of the logicians is, therefore,
founded on a blunder ; which is only doubled by the usual aver-
ment that the predicate, in what are technically called i^eciprocal
propositions, is taken universally vi materia: and not viformce.
But, 4°, The non-quantification of the predicate in thought is
given up by the logicians themselves, but only in certain cases
where they were forced to admit, and to the amount which they
could not possibly deny. The predicate, they confess, is quanti-
fied by particularity in affirmative, by universality in negative,
propositions. But why the quantification, formal quantification,
should be thus restricted in thought, they furnish us with no valid
reason.
To these two errors I might perhaps add as a third, the confu-
sion and perj^lexity arising from the attempt of Aristotle and the
logicians to deal with indefinite, (or, as I would call them, indesig-
nate), terms, instead of treating them merely as verbal ellipses, to
be filled up in the expression before being logically considered ;
and I might also add as a fourth, the additional comjilexity and
perplexity introduced into the science by viewing propositions,
likewise, as affected by the four or six modalities. But to these
I shall not advert.
These are the two principal errors which have involved our
systems of Logic in confusion, and prevented their evolution in
simplicity, harmony, and completeness ; — which have condemned
them to bits and fragments of the science, and for these bits and
fragments have made a load of rules and exceptions indispensable, to
avoid falling into frequent and manifest absurdity. It was in
reference to these two errors chiefly, that I formerly gave you as a
self-evident Postulate of Logic — " Explicitly to state what has been
implicitly thought ; " in other words, that before dealing logically
with a proposition, we are entitled to understand it, that is, to
204 APPENDIX.
ascertain and to enounce its meaning. This quantification of the
predicate of a judgment, is, indeed, only tlie beginning of the appli-
cation of the Postulate ; but we shall find that at every step it
enables us to cast away, as useless, a multitude of canons, which
at once disgust the student, and, if not the causes, are at least the
signs, of imperfection in the science.
I venture then to assert, that there is only one species of Con-
version, and that one thorough-o-oino; and self-sufficient. I mean
Pure, or Simple Conversion. The other species, — all are admitted
to be neither thorough-going nor self-sufficient, — they are in fact
only other logical processes, accidentally combined with a transpo-
sition of the subject and predicate. The conversio per accidens
of Boethius, as an Ampliative operation, has no logical existence ;
it is material and precarious, and has righteously been allowed to
drop out of science. It is now merely an historical curiosity. As
a Restrictive operation, in which relation alone it still stands in our
systems, it is either merely fortuitous, or merely possible through
a logical process quite distinct from Conversion, I mean that of
Eestriction or Subaltei-nation, which will be soon explained. Con-
verslo per contraposltioneiii is a change of terras, — a substitution
of new elements, and only holds through contradiction," being just
as CTOod without as with conversion. The Contino-ent Conversion
a. [See Ai'istotle, Tupica, L. ii. c. With the single exce^jtiuii of E u E (A
8. Scotus, Bauues, Mendoza, silently n A) the other seven propositions may
following each other, have held that be converted by Counterposition under
contraposition is only mediate, infinita- the following rule, — ' Let the terms be
tion, requiring Constantia, &c. Wholly infinitated and transposed, the predesig-
wrong. See Arriaga. — Curms Ph'doso- nations remaining as before.'
phicus, D. II. s. 4. p. 18. [" Observau- With the two additional exceptions
dum est prtedictas consequentias (per of the two convertible propositions,
contrapositionem) malas esse et insta- A f I, and I f A, the infinitated propo-
biles, nisi accesserit alia jjropositio in sitions hold good without the transposi-
antecedenti qune impartit existentiam tion of the terms,
subjecti fousequentis. Tunc enim firma Rule for Infinite Prejaceuts given,
erit consequentia, e.g. Omnis homo e^t With the single exception of n If n I,
albas et non album est, ergo omne non (nE = n = nE being impossible), the
album est non homo. Alioquin si con- other six propositions may be converted
stantiam illam non posueris in antece- by Counterposition under the following
denti, instabitur illi consequentiae in rule, — ' Let the terms be uninfinitated
eventu, in quo nihil sit non album, et and transposed, the predesignatious re-
omnis homo sit albus." Bannes, Inst'it. maining as before.'
Min. Dial. L. vi. c. 2, p. 530. — Ed.] Contraposition is not exphcitly evolved
Rule for Finite Prejacents given. by Aristotle in Prior Anabjtics, but is
APPENDIX.
2G5
of tlie lower Greeks " is not a conversion, — is not a logical process
at all, and has been worthily ignored by the Latin world. But
let us now proceed to see that Simple Conversion, as I have
asserted, is thorough-going and all-sufficient. Let us try it in
all the eight varieties of categorical propositions. But I shall
leave this explication to yourselves, and in the examination will
call for a statement of the simple conversion, as aj)plied to all the
eight propositional forms.
It thus appears, that this one method of conversion has every
advantage over those of the logicians. 1°, It is Natural ; 2°, It
is Imperative ; 3°, It is Simple ; 4°, It is Direct ; 5°, It is Pre-
cise ; 6°, It is Thorough-going : "Whereas their processes are — 1°,
evolved from his Tuples, L. ii. cc. 1, 8,
alibi. De Interpretatione, c. 14. See
Conimbricenses, In Arist. Dial., An.
Prior., L. I. q. i. p. 271. Bannes, Instit.
Minm^s Bialectlcfv, L. v. c. 2, p. 532.
Burgersdicius, Instit. Log. L. i. c. 32.
First explicitly enounced by Averroes
according to Molinaeus, {Ekmenta Lorji-
ca, L. i. c. 4, p. 54). I cannot find any
notice of it in Averroes. He ignores it,
name and thing. It is in Anonymus,
De Syllogismo, f. 42 b., in Nicephorus
Blemmidas, Epit. Log., c. xxxi. p. 222 ;
but long before him Boethius has all
the kinds of Conversion, — Simplex, Per
Acciclens, et Per Oppositionem {Intro-
ductio ad Sijllogismos, p. 576), what he
calls Per Contrapositionem, (De Syllo-
f/lsmo Categorico, L. i. 589.) Is he the
inventor of the name ? It seems so.
Long before Boethius, Apuleius, (in
second century), has it as one of the five
species of Conversion, but gives it no
name — only descriptive, see Dellahittid.
Doct. Plat., L. lii. p. 33. Alexander, In
An. Pr., i. c. 2, f. 10 a, has it as of pro-
positions, not of terms, which is con-
version absolutely. Vide Philoponus, In
An. Pr., I. f. 12 a. By them called avTi-
CTpocp)) (Tvv ai/TLOecet. So Magentinus,
In An. Prior., i. 2, f. 3 b.
That Contraposition is not properly
Conversion — (this being a species of con-
sequence) — an sequipoUence of pi'oposi-
tions, not a conversion of their terms.
Noldius, Logica Recognita, c. xii. p.
299. Crakanthorpe, Logica, L. iii. c.
10, p. 180. Bannes, Instit. Min. Dial.,
L. V. c. 2, p. 530. Eustachius, Summa
Philosophice, Lo/jica, P. II. tract, i. q. 3,
p. 104. Herbart, Lehrhuch der Logik,
p. 78. Scotus, Qiicestiones, In An. Prior.,
L. i. q. 15, f. 258 b. Chauvin, v. Con-
'versio. Isendoorn, Cursus Logicus,^). 308.
That Contraposition is useless and
^lerplexing. See Chauvin, v. Conversio.
Arriaga, Cursus, PhilosopKicus, p. 18.
Titius,^ rs Cogitandi, c. viii. § 19 e< seq.
D'Abra de Raconis, Tot. Phil. Tract.,
Logica, ii. q. 4, p. 315. Bannes, Instit.
Min. Dial, Yi. 529.]
o [Blemmidas.] [Epitome Logica, c.
31, p. 222. The following extract
will explain the nature of this con-
version. 'H 5' iv irpoTo.ffea'i yivo^lvi)
avTLarpocp^, f] r^v fiev Ta^iv tuv Spccu
(pvAarrei, rhy avrhv rripovaa Karriyopov-
fxsvov KoL rhv axnhv inroKeiixevov • fi6vi]V
Se TT]V 7roj(5T7jTa fiera^aWfi, Troiovffa t^jv
a,iTo(parLKi)v Trpuraaiv Kara(pa.riKi]V, koli
KaratpaTLKT^v airo(paTLKriv. Kal KeyeTai
avTY] iySexo/^^vri avTiarpocpi], ws tTri ix6vris
TTjS ivSexo/J-evvs v\7]s avvLaTaixivf) • oTov,
TLS avOpooTTos \overai, tis ^.^OpooTvos ov \ov-
erai • avrr] S' ovk av ety) Kvpioos avTt-
ffTpotp-f). This so-called contingent con-
version is in fact nothing more than the
assertion, repeated by many Latin logi-
cians, that in contingent matter subcon-
trary propositions are both true. — Ed.]
266 APPENDIX.
Unnatural ; 2°, Precarious ; 3°, Complex ; 4°, Circuitous ; 5°, Con-
fused ; 6°, Inadequate : breaking down in each and all of their
species. The Greek Logicians, subsequent to Aristotle, have well
and truly said, dpTLcrTpocfut] ecxTiv IcTocrTpo^rj rt? " omnis conversio
est ajquiversio" * that is, all conversion is a conversion of equal into
equal ; and had they attended to this principle, they would have
developed conversion in its true unity and simplicity. They would
have considered, 1°, That the absolute quantity of the proposi-
tion, be it convertend or converse, remains always identical ; 2"*,
That the several quantities of the collated notions remain always
identical, the whole change being the transjjosition of the quanti-
fied notion, which was in the subject place, into the place of pre-
dicate, and vice versa.
Aristotle and the logicians were, therefore, wrong; 1°, In not
considering the proposition simply as the complement, that is, as
the equation or non-equation, of two compared notions, but, on the
contrary, considering it as determined in its quantity by one of
these notions more than by the other. 2°, They were wrong, in
according too great an imj)ortance to the notions considered as pro-
positional terms, that is, as subject and predicate, independently
of the import of these notions in themselves. 8°, They were
wrong, in according too preponderant a weight to one of these
terms over the other ; but difierently in different parts of the
system. For they were wrong, in the doctrine of Judgment, in
allowing the quantity of the proposition to be determined exclu-
sively by the quantity of the subject term ; whereas they were
wrong, as we shall see, in the doctrine of Reasoning, in considering
a syllogism as exclusively relative to the quantity of the predicate
(extension). So much for the theory of Conversion. Before con-
cluding, I have, however, to observe, as a correction of the preva-
lent ambiguity and vacillation, that the two j)roi30sitions of the
process together might be called the convertent or converting, (pro-
2)ositiones convertentes) ; and whilst of these the original proposi-
tion is named the convertend [propositio convertenda), its product
would obtain the title oi converse, converted, (propositio conversd).^
The other species of Immediate Inference will not detain us
long. Of these, there are two noticed by the logicians.
a See above, p. 256. — Eu. fi See above, vol. i. p. 262. — Ed.
APPENDIX. 2G7
Tlie first of these, EquipoUence, (cequipoUentid), or, as I would
term it, Double Negation, is deserving of bare mention. It is of
mere grammatical relevancy. The negation of a negation is tanta-
momit to an affirmation. B is not not-A, is manifestly only a
roundabout way of saying B is A ; and, vice versa, we may express
a position, if we perversely choose, by sublating a sublation. The
immediate inference of Equipollence is thus merely the grammati-
cal translation of an affirmation into a double negation, or of a
double negation into an affirmation. Non-nullus and Non-nemo^
for example, are merely other grammatical expressions for aliquis
or quidam. So Nonnihil, Nonnunquam, Nonnusquam, &c.
The Latin tongue is almost peculiar among languages for such
double negatives to express an affirmative. Of course the few
which have found their place in Logic, instead of being despised
or relegated to Grammar, have been fondly commented on by the
ingenuity of the scholastic logicians. In English, some authors
are fond of this indirect and idle way of speaking ; they prefer
saying — "I entertain a not unfavourable opinion of such a one,"
to saying directly, I entertain of him a favourable opinion.
Neglecting this, I pass on to
The third species of Immediate Inference, noticed by the
logicians. This they call Subalternation, but it may be more
unambiguously styled Restriction. If I have £100 at my credit
in the bank, it is evident that I may draw for £5 or £10. In like
manner, if I can say unexclusively, that all men are animals, I can
say restrictively, that negroes or any other fraction of mankind are
animals. This restriction is Bilateral, when we restrict both sub-
ject and predicate, as —
All Triangle is all trilateral. All rational is all risible.
.: Some triangle is some trilateral. .: Some rational is some risible.
It is Unilateral, by restricting the omnitude or universality either
of the Subject or of the Predicate.
Of the Subject—
All man is some animal;
.'. Some man is some animal.
Of the Predicate, as —
268 APPENDIX.
Some animal is all risible
,: Some animal is some risible.
It has not been noticed by the logicians, that there is only an
inference by this process, if tlie some in the inferred proposition
means some at least, that is, some not exclusive of all; for if we
think by the some, some only, that is, some, not all, so far from
there being any competent inference, there is in fact a real opposi-
tion. The logicians, therefore, to vindicate their doctrine of the
Opposition of Subalternation, ought to have declared, that the some
was here in the sense of some only ; and to vindicate their doctrine
of the Inference of Subalternation, they ought, in like manner, to
have declared, that the some was here taken in the counter sense
of some at least. It could easily be shown, that the errors of the
logicians in regard to Oj)position, are not to be attributed to
Aristotle.
Before leaving this process, it may be proper to observe that we
might well call its two propositions together the restringent or
restrictive, {lyrojwsitiones 7'estringentes vel restrictivce) ; the given
proposition might be called the restringend, (propositio restrin-
genda), and the product the 7'estrict or restricted, {propositio
restricta.)
So much for the species of Immediate Inference recognised by
the logicians.
There is, however, a kind of immediate inference overlooked by
logical writers. I have formerly noticed, that they enumerate,
(among the species of Opposition), Suhcontrariety, (subcontrarietas,
VTrevavTLOTT]'!;), to wit, — some is, some is not ; but that this is not
in fact an opposition at all, (as in truth neither is Subalterna-
tion in a certain sense.) Suhcontrariety, in like manner, is with
them not an opposition between two partial somes, but between
different and different ; in fact, no opposition at all. But if they
are thus all wrong by commission, they are doubly wrong by
omission, for they overlook the immediate inference which the
relation of propositions in Suhcontrariety affords. This, however,
is sufficiently manifest. If I can say, All men are some animals,
or, Some animals are all men, I am thereby entitled to say, —
All men are not some animals, or Some animals are not some
men. Of course here the some in the inferred propositions means
APPENDIX. 269
some other, as in the original proposition, some only ; but the
inference is perfectly legitimate, being merely a necessary explica-
tion of the thought : for inasmuch as I think and say that all men
are some animals, I can think and say that they are some animals
only, which implies that they are a certain some, and not any
other animals." This inference is thus not only to some others
indefinitely, but to all others definitely. It is further either afiirma-
tive from a negative antecedent, or negative from an aflirmative.
rinally, it is not bilateral, as not of subject and predicate at
once ; but it is unilateral, either of the subject or of the predi-
cate. This inference of Subcontrariety, I would call Integration,
because the mind here tends to determine all the parts of a whole,
whereof a part only has been given. The two propositions toge-
ther might be called the integral or integrant, {propositiones
integrales vel integrantes). The given proposition would be styled
the integrand, {'propositio integranda) ; and the product, tlie
integrate, {propositio integrata). p
I may refer you for various observations on the Quantification
of the Predicate, to the collection published under the title,
Discussions on Philosophy and Literature.
The grand general or dominant result of the doctrine on which
I have already partially touched, but which I will now explain
consecutively and more in detail, is as follows : — Touching Proposi-
tions, — Subject and Predicate ; — touching Syllogisms, — in Catego-
ricals, Major and Minor Terms, Major and Minor Premises, Figures
First, Second, Third, Fourth, and even what I call ISfo Figure, are
all made convertible with each other, and all conversion reduced to a
simple equation ; whilst in Hypotheticals, both the species, (viz.
Conjunctive and Disjunctive reasonings), are shown to be forms
a If we say some animal is all man, Therefore, some animals are not some
and some animal is not amy man; in that animals.
case, we must hold some as meaning fi Mem. Immediate inference of Con-
some only. We may have a mediate tradictiou omitted. Also of Relation,
syllogism on it, as : which would come under Equipollence.
[For Tabular Schemes of Propositional
Some animals are all men ; Forms, and of their Mutual Relations,
Some animals are not any man; see below, i>p. 277, 278. — Ed.]
270 APPENDIX.
not of mediate argumentation at all, but merely complex varieties
of the immediate inference of Eestriction or Subalternation, and
are relieved of a load of perversions, limitations, exceptions, and
rules. The differences of Quantity and Quality, &c. thus alone
remain ; and by these exclusively are Terms, Propositions, and
Syllogisms formally distinguished. Quantity and Quality combined
constitute the only real discrimination of Syllogistic Mood. Syllo-
gistic Figure vanishes, with its perplexing apparatus of special
rules ; and even the General Laws of Syllogism proper are reduced
to a single compendious canon.
This doctrine is founded on the postulate of Logic : — To state
in language, what is efficient in thought ; in other words, Before
proceeding to deal logically with any proposition or syllogism, we
must be allowed to determine and express what it means.
First, then, in regard to Propositions. — In a proposition, the
two terms, the Subject and Predicate, have each their quantity in
thought. This quantity is not always expressed in language, for
language tends always to abbreviation ; but it is always under-
stood. For example, in the proposition, Men are animals, what
do we mean? We do not mean that scyne men, to the exclusion
of others, are animals, but we use the abbreviated expression
inen for the thought all men. Logic, therefore, in virtue of
its postulate, warrants, nay requires, us to state this explicitly.
Let us, therefore, overtly quantify the subject, and say, All men
are animals. So far we have dealt with the proposition, —
we have quantified in language the subject, as it was quantified
in thought.
But the predicate still remains. We have said — A U men are
animals. But what do we mean by animals ? Do we mean all
animals, or some animals ? Not the former ; for dogs, horses,
oxen, &c. are animals as well as men, and dogs, horses, oxen, &c.
are not men. Men, therefore, are animals, but exclusively of dogs,
horses, oxen, &c. All men, therefore, are not equivalent to all
animals ; that is, we cannot say, as we cannot think, that all men
are all animals. But we can say, for in thought we do affirm,
that all men are some animals.
But if we can say, as we do think, that all men are some
anim.als, we can, on the other hand, likewise say, as we do think,
that some animals are all m,en.
APPENDIX. 271
If this be true, it is a matter of indifference, in a logical point
of view, (whatever it may be in a rhetorical), which of the two
terms be made the subject or predicate of the proposition ; and
whichsoever term is made the subject in the first instance, may,
in the second, be converted into the predicate, and whichsoever
term is made the predicate in the first instance, may, in the
second, be converted into the subject.
From this it follows : —
1°, That a proposition is. simply an eqnation, an identification,
a bringing into congruence, of two notions in respect to their
Extension. I say, in respect to their Extension, for it is this quan-
tity alone which admits of ampliation or restriction, the Compre-
hension of a notion remaining always the same, being always taken
at its amount.
2°, The total quantity of the proposition to be converted, and
the total quantity of the jiroposition the product of the conver-
sion, is always one and the same. In this unexclusive point of
view, all conversion is merely simple convei-sion ; and the dis-
tinction of a conversion, as it is called, by accident, arises only
from the partial view of the logicians, who have looked merely to
the quantity of the subject. They, accordingly, denominated a pro-
position universal or particular, as its subject merely was quanti-
fied by the predesignation some or all ; and where a proposition
like, All men are animals, (in thought, some animals), was con-
verted into the proposition, Some animals are men, (in thought,
all men), they erroneously supposed that it lost quantity, was re-
stricted, and became a particular proposition.
It can hardly be said that the logicians contemplated the re-
conversion of such a proposition as the preceding ; for they did
not (or rarely) give the name of conversio 'per accidens to the case
in which the proposition, on their theory, was turned from a par-
ticular into a universal, as when we reconvert the proposition.
Some animals are men, into the proposition. All men are ani-
mals.^ They lili:ewise neglected such affirmative propositions as
o See above, vol. i. p. 264. — Ed. [A lius, Logica, t. ii. 1. i. q. i. c. 2, p. 32. For
mistake by logicians in general, that Aristotle xises the terms universal, and
partial conversion, eV /uepei, is the mere partial conversion, simply to express
synonym of x>er accidens, and that the whether the convertens is an universal or
former is so used by Aristotle. See Val- particular proposition. See § 4 of the
272 ArPENDIX,
had ill thought both subject and predicate quantified to their
whole extent ; as, All triangular figure is trilate7xd, that is, if
expressed as understood, All triangular is all trilateral figure, —
All rational is risible, that is, if explicitly enounced, All rational
is all risible animal. Aristotle, and subsequent logicians, had
indeed frequently to do with propositions in which the predicate
was taken in its full extension. In these the logicians, — but, be it
observed, not Aristotle, — attempted to remedy the imjjerfection of
the Aristotelic doctrine, which did not allow the quantification of
the predicate to be taken logically or formally into account in
affirmative propositions, by asserting that in the obnoxious cases
the predicate was distributed, that is, fully quantified, in virtue of
the matter, and not in virtue of the form, (vi materiw, non ratione
formce). But this is altogether erroneous. Por in thought we
generally do, nay, often must, fully quantify the predicate. In our
logical conversion, in fact, of a proposition like All men are
aniinals, — some animals, we must formally retain in thought,
for we cannot formally abolish, the universal quantification of
the predicate. We, accordingly, must formally allow the propo-
sition thus obtained, — Some animals are all m.en.
The error of the logicians is further shown by our most naked
logical notation ; for it is quite as easy and quite as natural to
quantify A, B, or C, as predicate, as to quantify A, B, or C, as
subject. Thus, All^ is some A ; So7ne A is all B.
A, -.B
I may here also animadvert on the counter defect, the counter
chapter on Conversion, {An. Prior., i. 2), ]ess,orfrom less to greater,s«?r« reritate,
■\\ here particuhir affirmatives are said to the quality of the terms and projiosi-
be necessarily converted, iv fiepei. tions remaining always the same. So
Conversio ^5fr accidcvs is in two forms Ridiger, Z>e Sensu Veri et Falsi, p. 303.
differently defined by different logicians. The second is that of logicians in gene-
The first by Boethius, by whom the name ral, where the quantity of the proposi-
was originally given, is that in which the tion is diminished, the quality of the
quantity of the proposition is contin- propositions and terms rem.aiuing the
gently changed either from greater to same, salva reritate.]
APPENDIX. 273
error, of the logicians, in their doctrine of Negative Propositions.
In negative propositions they say the predicate is always distri-
buted, — always taken in its full extension. Now this is altogether
untenable. For we always can, and frequently do, think the pre-
dicate of negative propositions as only partially excluded from the
sphere of the subject. For example, we can think, as our naked
diagrams can show, — All men are not some ammals, that is, not
irrational animals. In point of fact, so often as we think a sub-
ject as partially included within the sphere of a predicate, eo ipso
we think it as partially, that is, jjarticularly, excluded therefrom.
Logicians are, therefore, altogether at fault in their doctrine, that
the predicate is always distributed, i.e. always universal, in negative
propositions. "
But, 3°, If the preceding theory be true, — if it be true that sub-
ject and predicate are, as quantified, always simply convertible,
the proposition being in fact only an enouncement of their equa-
tion, it follows, (and this also is an adequate test), that we may at
will identify the two terms by maldng them both the subject or
both the predicate of the same proposition. And this we can do.
For we can not only say — as A is B, so conversely B is A, or as
All 7716)1 are some animals, so, conversely, Some animals are all
men; but equally say — A and^ are convertible, or. Convertible
are B and A; All men and some animals are convertible, (that is,
a [Melanchthou, (Erotemata, L. li. Be both subject and predicate, in other
Conversione, p. 516), followed by his words, to the whole proposition,
pupil and commentator Strigelius, {In This doctrine is altogether erroneous.
Erotemata, pp. 576, 581), and by Keck- It is an erroneous theory devised to
ermann, {Syst. Log. Minus, L. ii. c. 3, Op. explain an erroneous pi'actice. In the
p. 222), and others, thinks that " there first place, we have here a commutation
is a greater force of the particle none, of negation with quantification ; and, at
{nullus, not any), thunoi the Tpa^rticle all, the same time, conversion, direct con-
{omnis). For, in a universal negative, version at least, will not be said to
the force of the negation is so spread change the quality either of a negative
over the whole proposition, that in its or affirmative proposition. In the se-
conversion the same sign is retained, (as cond place, it cannot be pretended that
— No star is consumed; therefore, no negation has an exclusive or even greater
fiame ivhich is consumed is a star) : affinity to \iniversal than to particu-
whereas such conversion does not take lar quantification. We can equally well
place in a univei-sal affirmative." This say not some, not all, not any; and the
Strigelius compares to the diffusion of reason why one of these forms is pre-
a ferment or acute poison ; adding that ferred, lies certainly not iu any attrac-
the affirmative particle is limited to the tion or aflSnity to the negative par-
subject, whilst the negative extends to tide.]
VOL. TI. S
274
APPENDIX.
some convertible things), or, Convertible, (that is, some convertible
things), are some animals and all men. By convertible, I mean
the same, the identical, the congruent, &c.a
The general errors in regard to Conversion, — the errors from
which all the rest proceed, are —
1°, The omission to quantify the predicate throughout.
2°, The conceit that the quantities did not belong to the terms.
3°, The conceit that the quantities were not to be transposed
with their relative terms.
4°, The one-sided view that the proposition was not equally
composed of the two terms, but was more dependent on the sub-
ject than on the predicate.
0°, The consequent error that the quantity of the subject term
determines the quantity of the proposition absolutely.
a [With tbe doctrine of Conversion
taught in the text, compare the follow-
ing authorities ; — ■ Laurentius Valla,
Dialectica, L. ii. c. 24, f. 37. Titius,
Ars Cogitandi, (v. Ridiger, De Sensu
Veri et Falsi, L. ii. c. i. p. 232).
Reusch, Systema Logknm, § 380, p. 413
et seq., ed. 1741. Hollmanu, Lorjica, § 89,
p. 172. Ploucquet. Fries, Logik, § 33,
p. 146. E. Reinhold, Looik, § 117, p.
286, Ancients referred to by Am-
monius, In De InUrp., c. vii., § 4, f. . . .
Paulus Vallius, Logica, t. ii., In An.
Prior., L. i. q. ii. c. iv.] [Valla I. c.
says : — " Non amplius ac latins aceipitur
prtedicatum quam subjectum. Ideoque
cum illo converti potest, ut omnis homo
est animal: non utique totum genus
animal, sed aliqua pars hujus generis . .
ergo, Aliqua pars animalis est in omni
homine. Item, Quidam homo est ani-
mal, scilicet est qucedam pars animalis,
ergo, Qucedam pars animalis est qtiidam
homo, &c." Gottlieb Gerhard Titius,
Ars Cogitandi, c. vii. § 3 c< seq., p. 125.
Lipsise, 1723 (first ed. 1701). " Nihil
autem aliud agit Conversio, quam ut
simpliciter pra3dicatum et subjectum
transponat, hinc nee qualitatem nee
quantitatem iis largitur, aut eas mutat,
sed prout reperit, ita convertit. Ex
quo necessario sequitur conversionem
esse uniformem ac omnes propositiones
eodem plane mode converti. Per ex-
empla, (1), Nullus homo est lapis, ergo,
Nullus laptis est homo, (2), Quidam homo
non est medicus (omnis), ergo, Medicus
non est homo quidam, seu Nullus medicus
est homo quidam . . . (3), Hie Petrxos
non est doctus (omnis), ergo, Omnis doc-
tus nonesthic Petrus . . . (4), Omnis
homo est animal (quoddam), ergo. Quod-
dam animal est homo (5), Quidam homo
currit (particulariter), ergo, Quidam cur-
rens est homo, (6), Hie Paulus est docttis
(quidam), ergo, Quidam doctus est hie
Paulus. In omnibus his exemplis sub-
jectum cum sua quantitate in locum
praadicati, et hoc, eodem modo, in illius
sedem transponitur, ut nulla penitus
ratio solida appareat, quare conversi-
onem in diversas species divellere de-
beamus. Vulgo tamen aliter sentiunt
quando triplicem conversionem, nempe
simplicem, per accidens, ac pjer eontra-
p)ositionem, adstruunt. . , . Enimvero
conversio per accidens et per contraposi-
tionem gratis asseritur, nam conversio
APPENDIX.
275
(j°, The consequent error that there was any increase or dimi-
nution of the total quantity of the proposition.
7°, That thoroughgoing conversion could not take place by one,
and that the simple, form.
8°, That all called in at least the form of Accidental Conversion ;
all admitting at the same time that certain moods remain incon-
vertible.
9°, That the majority of logicians resorted to Contraposition,
(which is not a conversion at all) ; some of them, however, as
Burgersdyk, admitting that certain moods still remained obstinately
inconvertible.
10°, That they thus introduced a form which was at best indi-
rect, vague, and useless, in fact not a conversion at all.
1 ] °, That even admitting that all the moods were convertible
by one or other of the three forms, the same mood was convertible
by more than one.
propositionis aiBrmantis viniversalis per-
inde simplex est ac ea qua universalis
negans convertitur, licet post earn sub-
j actum sit particulare ; conversionis
enim hie nulla culpa est, qute quanti-
tatem, quae non adest, largiri nee potest
nee debet. . . . Error vulgaris doctrinaj,
nisi fallor, inde est, quod esistimaverint
ad conversionem simplicem requiri, ut
pradicatum assumat signuni et quantita-
tem subjecti . . . Conversionem ^:)er
contrapositionem quod attinet, facile os-
tendi potest (1) exempla heic jactari
solita, posse converti simf)liciter ; (2)
conversionem per contrapositionem, re-
vera non esse conversionem ; intei'im (3)
putativam istam conversionem non in
universali afBrmante, et particulari ne-
gante solum, sed in omnibus potius pro-
positionibus locum habere . , . e.g.,
Quoddam animal non est quadrupes, ergo,
Nidlus quadrupes est animal quoddam."
See the criticism of the doctrine of
Titius by Ridiger, quoted below, p. 311.
Ploucquet, Methodus Calculandi in
Logicis, p. 49 (1763). " Intellectio identi-
tatis subjecti et preedicati est aj[jirmatio.
• . . Omnis circulus est linea curva.
Qua) propositio logice expressa ha^c est :
— Omnis circulus est qvcedam linea curva.
Quo pacto id, quod intelligitur in prsedi-
cato identificatur cum eo quod intelligitur
in subjecto. Sive norim, sive non norim
prseter circulum dari quoque alias cur-
varum species, verum tamen est quan-
dam lineam curvam sensu comprehensivo
sumtam, esse omnem circulum, seu om-
nem circulum esse quandam lineam cur-
vam." Vallius, I. c. " Negatives vero
convertuntur et in j^articulares et in
universales negativas ; ut si dicamus,
Socrates non est lapis, convertens illius
erit, Aliquis lapis non est Socrates, et
Nullus lapis est Soa'ates, et idem di-
cendum erit de omui alia simili proposi-
tione." — Ed.]
[That Universal Affirmative Proposi-
tions may be converted simply, if their
pi-edicates are reciprocating, see Cor-
vinus, Instit. Phil. Rat., § 514. lense,
1742. Baumgarten, Logica, § 280,
1765. Scotus, In. An. Pr., L. i. qu.
14. Ulrich, Instit. Log. et Met.,
§ i. 2, 177, (1785). Kreil, LogiJc, §§ 46,
62, (1789). Isendoorn, Logica Peripa-
tctica, L. iii. c. 8, pp. 430, 431. Wal-
lis, Logica, L. ii. c. 7. Zabarella, In.
An. Prior. Tahulce, p. 148. Lambert,
Be Universaliori Calculi Idea, § 24 et
seq:\
276 APPENDIX.
1 2', That all this mass of error and confusion was from their
overlooking the necessity of one simple and direct mode of con-
version : missing the one straight road.
We have shown that a judgment (or proposition) is only a
comparison resulting in a congruence, an equation, or non-equa-
tion of two notions in the quantity of Extension ; and that these
compared notions may stand to each other, as the one subject and
the other predicate, as both the subject, or as both the predicate of
the judgment. If this be true, the transposition of the terms of
a projDOsition sinks in a very easy and a very simple process ;
whilst the whole doctrine of logical Conversion is superseded as
operose and imperfect, as useless and erroneous. The systems, new
and old, must stand or fall with their doctrines of the Conversion
of propositions.
Thus, according to the doctrine of the logicians, conversion
applies only to the naked terms themselves: — the subject and
predicate of the prejacent interchange places, but the quantity
by which each was therein affected is excluded from the move-
ment ; remaining to affect its correlative in the subjacent proposi-
tion. This is altogether erroneous. In conversion we transpose
the compared notions, — the correlated terms. If we do not, ever-
81071, not conversion, is the result.
If, (as the Logicians suppose), in the convertens the subject
and predicate took each other's quantity, the proposition would
be not the same relation of the same notions. It makes no
difference that the converse only takes place when the subject
chances to have an equal amount or a less than the predicate.
There must be at any rate a reasoning, (concealed indeed), to
warrant it : in the former case — that the predicate is entitled to
take all the quantity of the subject, being itself of equivalent
amount ; in the second, (a reasoning of subalternation), that it is
entitled to take the quantity of the subject, being less tlian its
own. All this is false. Subject and predicate have a right to
their own, and only to their own, which they carry with them,
when they become each other.
APPENDIX.
://
{d) APPLICATION OF DOCTRINE OF QUANTIFIED
PREDICATE TO PROPOSITIONS.
(1). New Pkopositional Forms — Notation.
Instead of four species of Proposition determined by the Quantity
and Quality taken together, the Quantity of the Subject being
alone considered, there are double that number, the Quantity of the
Predicate being; also taken into account.
(2B
Affirmative.
(1) [AfA] C:
(ii) [Afl] C::
(3) [If A] A,^
(iv) [If I] 0,:
Negative,
(v) [EnE]
( A) (A)
(6) [EnO] C:
(A) (I)
(vii) [OnE] B,
(I) (A)
(8) [OnO] C,
(I) (I)
- : r All Triangle is all Trilateral [fig. 1].
-, A AU Triangle is some Figure (A)
[fig- 2].
- : C Some Figure is all Triangle [fig. 2].
-•, B Some Triangle is some Equilateral
(I) [fig. 4].
: D Any Triangle is not any Square (E)
- , B Any Triangle is not some Equilateral
[fig. 4].
- : C Some Equilateral is not any Triangle
(0) [fig. 4].
- ,B Some Triangle is not some Equila-
teral [fig. 4].«
« [In this table the Roman numerals
(listingnish such prepositional forms as
are recognised in the Aristotelic or
common doctrine, whereas the Arabic
ciphers mark those (half of the whole)
which I think ought likewise to be
recognised. In the literal symbols, I
simplify and disintricate the scholastic
notation ; taking A and I for universal
and particular, but, extending them to
either qualit}% marking affirmation by f,
negation by n, the two first consonants
of the verbs affirmo and nego, — verbs
from which I have no doubt that Petnis
Hispanus drew, respectively, the two first
vowels, to denote his four complications
of quantity and quality.] — Discussions,
p. 686.
[In the notation emjjloyed above, the
comma , denotes some ; the colon : all ;
the line »=— denotes the affirmative
copula, and negation is expressed by
drawing a line through the affirmative
copula ia4~ J ^^s thick end of the line
278
APPENDIX.
(2). Quantity of Propositions — Definitude and
Indefinitude.
Nothing can exceed the ambiguity, vacillation, and uncertainty
of logicians concerning the Quantity of Propositions.
I. As regards what are called indefinite (aStoptcrrot more pro-
perly indesignate or preindesignate projwsitmis. The absence of
overt quantification applies only to the subject ; for the predicate
was supposed always in affirmatives to be particular, in negatives to
be universal. Keferring, therefore, only to the indesignation of the
subject : — indefinites were by some logicians, (as the Greek com-
mentators on Aristotle (?), Apuleius aptid Waitz, In Org. i. p.
338, but see Wegelin, In Aneponymi Phil. Syn., p. 588), made
tantamount to particulars : by others, (as Valla, Dialectica, L.
ii. c. 24, f. 37), made tantamount to imiversals. They ought
to have been considered as merely elliptical, and to be definitely
referable either to particulars or universals."
denotes the subject, the thin end the
predicate, of Extension. In Intension
the thin end denotes the subject, the
thick end the predicate. Thus : —
C : i^— , A is read, All C is some A.
C : H— : D is read, No C is any D. The
Table given in the text is from a copy
of an early scheme of the author's new
Prepositional Forms. For some time
after his discovery of the doctrine of a
quantified predicate, Sir W. Hamilton
seems to have used the vowels E and
O in the formula) of Negative Proposi-
tions ; and the full period (.) as the
symbol of some (indefinite quantity). In
the college session of 1845-46, he had
adopted the comma (,) as the symbol of
indefinite quantity. As the period ap-
pears in the original copy of this table
as the symbol of some, its date cannot
be later than 1845. The comma (,) has
been substituted by the Editors, to adapt
the table to the Author's latest form of
notation. The translation of its symbols
into concrete propositions, affords deci-
sive evidence of the meaning which the
Author attached to them on the new
doctrine. That this, moreover, was the
tmiform import oi Sir W. Hamilton's
prepositional notation, from the earliest
development of the theoi-y of a quantified
predicate, is placed beyond doubt by
numerous passages in papei-s (not print-
ed), and b}^ marginal notes on books,
written at various periods between 1839-
40, and the date of his illness, July 1844,
when he was compelled to employ an
amanuensis. The letters in round brack-
ets, (A) and (I), are the vowels finally
adopted by the Author, in place of E and
0. See below, p. 283, Ed.]
a [That Indefinite propositions are to
be referred to universals, see Purchot,
Instit. Phil. Lof/ica, I. § ii. c. 2, pp. 124,
125, 126. Kottenbeccius, Logirn Con-
tracta, c. vi. p. 92, (1560). Baumeister,
Inst. Phil. Rat., § 213. J. C. Scaliger,
Exercitationes, Ex. 212, § 2. Drobisch,
Logik, § 39. Neomagus, Ad Traiiezun-
tium, f. 10. To be referred to particular;
see Lovanienses, Com. in Arist. Dial. p.
161. MolinEeus, Elementa Logica, L. I.
c. 2. Alex. Aphrod, In An. Prior., c. ii.
p. 19. Denzinger, Logica, § 71. Either
universal or particular, Keckermann,
Opera, p. 220. Aristotle doubts : see
An. Prior, L. I. c. 27, •§ 7, and Be
Intcrp. c. 7. That Indefinitude is no
separate species of quantity, see Schei-
bler. Opera Logica, p. iii. c. 6, p. 443.
Grgecus Anonymus, De Si/llogismo, L.
i. c. 4, f. 42. Leibnitz, Opera, t. iv.
APPENDIX. 279
II. A remarkable uncertainty prevails in regard to the meaning
of particularity and its signs, — some, &c. Here some may mean
some only — some not all. Here some, though always in a certain
degree indefinite, is definite so far as it excludes omnitude, — is used
in opposition to all. This I would call its Semi-definite meaning.
On the other hand, some may mean some at least, — some, perhaps
all. In this signification some is thoroughly indefinite, as it does
not exclude omnitude or totality. This meaning I would call the
Indefinite.
Now of these two meanings there is no doubt that Aristotle used
particularity only in the second, or thoroughly Indefinite, meaning.
For 1°, He does not recognise the incompossibility of the super-
ordinate and subordinate. 2°, He makes all and ov Tra? or particu-
lar negative, to be contradictories ; that is, one necessarily true, the
other necessarily false. But this is not the case in the Semi-definite
meaning. The same holds good in the Universal Negative, and
Particular Affirmative.
The particularity, — the some, — is held to be a definite soTne when
the other term is Definite, as in ii and 3, in 6 and vii. On the
other hand, when both terms are Indefinite or Particular, as in iv.
and 8, the some of each is left wholly indefinite.
The quantification of definitude or non-imrticidarity (:) may
designate ambiguously or indifferently one or other of three con-
cepts. 1°, It may designate explicit omnitude or totality ; which,
when expressed articulately, may be denoted by (::). Thus — All
tria7igles are all trilatei'als. 2°, It may designate a class con-
sidered as undivided, though not positively thought as taken in its
whole extent ; and this may be articulately denoted by (:.). Thus
— The triangle is the trilateral ; — The dog is the lati'ant. —
(Here note the use of the definite article in English, Greek, French,
German," &c.) 3°, It may designate not what is merely undivided,
p. iii. p. 123. Fries, System der Lof/ik, logical import, when we do not know
§ 30, p. 137. Eamus, Schol. Dial., L. whether all, or some, of the one be to
vii. c. 2, p. 457. Downam, Jn Rami be affirmed or denied of the other. E.
Dialect., L. ii. c. 4, p. 359. Facciolati, Reinhold, Lo'jik, § 88. Anm. 2, pp. 193,
Rud. Log. p. ii. c. iii., p. 67. Delari- 194. Ploucquet, Methodus Calcidandi,
y'lhre, Nouvelle Logique Classique, h. ii. pp. 48, 53, ed. 1773. Lambert, Neues
s. ii. c. 3, s. 580, p. 334. Organon, I., § 235, p. 143.]
That Indefinitude has sometimes a a [On effect of the definite article and
280
APPENDIX.
though divisible, — a class, but what is indivisible, — an individual ;
and this may be marked by the small letter or by (:) — Thus
— Socrates is the hushand of Xanthijipe ; — This horse is
Bucephalus.
In like manner particularity or indefinitude (,), when we wish
to mark it as thoroughly indefinite, may be designated by (',),
whereas when we would mark it as definitely indefinite, as ex-
cluding all or not any, may be marked by (").
The indefinites (aopiara) of Aristotle correspond sometimes to
the particular, sometimes to one or other, of the two kinds of
universals."
The designation of indefinitude or partictdarit>/, some (, or ,)
may mean one or other of two very different things.
1°, It may mean some and some only, being neither all nor none,
and, in this sense, it will be both affirmative and negative, (,,).
2°, It may mean, negatively, not all, perhaps none, some at
most; affirmatively, 7iO^ none, perhaps all, — some at least, (, ,).
Aristotle and the logicians contemplate only the second mean-
its absence in different languages, in re-
ducing the definite to tlie indefinite,
see Delariviere, Logique, §§ 580, 581.
On the Greek article, see Ammonivis,
In De Interp. c. vii. f. 67 b.
On use of the Arabic article in quan-
tification, see Averroes, De Interp., p.
39, ed. 1552 :—
" Al in the Arabic tongue, and Ha
in the Hebrew, and in like manner the
articles in other languages, sometimes
have the power of universal predesigna-
tions, sometimes of particular. If the
former, then they have the force of con-
traries ; if the latter, then the force of
sub-contraries. For it is true to say, al,
that is, /^3se Jiomo is white, and al, that
is, ijjse homo is 7iot white ; that is, when
the article al or ha, that is, ipse, denotes
the designation of particularity. They
may, however, be at once false, when
the article al or ha has the force of the
universal predesignation." (See also p.
52 of the same book.)
In English the definite article always
defines, — renders definite, — but some-
times individualises, and sometimes ge-
neralises. If we would use man gene-
rally, we must not prefix the article, as
in Greek, German, French, &c., so wealth,
government, &c. But in definition of
horse. Sec, the reverse, as the dog, (le
chien, 6 kvuv, &c.) A in English is often
equivalent to anyP\
a [Logicians who have marked the
Quantities by Definite, Indefirate, &c.
Aristotle, A)i. Pr. c. iv. § 21, and
thei'e Alexander, Pacius. Theophras-
tus, (Facciolati, Riid. Log., p. i. c. 4,
p. 39.) Ammonius, In De Inter., f. 72 b.
(Brandis, Scholia, p. 113.) Stoics and
Non-peripatetic Logicians in general,
see Sext. Empiricus, Adv. Log., § 98
ef seq., p. 476, ed. Fabricii ; Diog.
Laert. Lib. vii. seq. 71, ubi Menagius.
Dowuam, In Hami Dialecticam, L. ii.
c. 4, p. 363, notices that a parti-
cular proposition " was called by the
Stoics indefinite, {aipiffrov) ; by some
Latins, and sometimes by Ramus him-
self, infinite; because it does not de-
signate some certain species, but leaves
it uncertain and indefinite." Hurtado de
Mendoza, Dis^). Log. et Met., t. i. d. iv. §
APPENDIX. 281
ing. The reason of this perhaps is, that this distinction only
emerges in the consideration of Opposition and Immediate Infer-
ence, which were less elaborated in the former theories of Logic ;
and does not obtrude itself in the consideration of Mediate Infer-
ence, which is there principally developed. On the doctrine of the
logicians, there is no opposition of snbalternation ; and by Aris-
totle no opposition of snbalternation is mentioned. By other
logicians it was erroneously introduced. The opposition of Sub-
contraries is, likewise, improper, being precarious and not between
the same things. Aristotle, though he emmierates this opposition,
was quite aware of its impropriety, and declares it to be merely
verbal, not real."
By the introduction of the first meaning of some, we obtain a
veritable opposition in Snbalternation ; and an inference in Sub-
contrariety, which I would call Integration.
(3.) Opposition of Peoposittons.
Propositions may be considered under two views ; according as
their particularity, or indefinitude, is supposed to be thoroughly
indefinite, unexclusive even of the definite ; some, meaning some
at least, some, perhaps all, some, perhaps not any ; or definite
indefinitude, and so exclusive of the definite ; some, meaning some
at most, — some only, — some not all, &c. The latter thus excludes
omnitude or totality, positive or negative ; the former does not.
The former is the view promulgated as alone contemplated by
Aristotle ; and has been inherited from him by the Logicians, with-
out thought of increase or of change. The latter is the view which
I would introduce ; and though it may not supersede, ought, I
think, to have been placed alongside of the other.
Causes of the introduction of the Aristotelic system alone : —
1°, To allow a harmony of Logic with common language ; for
language eliding all that is not of immediate interest, and the
determination of the subject-notion being generally that alone
intended, the predicate is only considered in so far as it is thought
to cover the subject, that is, to be at least co-extensive with it.
2, p. 114. 'LoY&menaes,, In Arist. Dial., \>. a On both forms of Opposition, see
161. Hollmann,Zo^/ca,p. 173. Boethius, Scheibler, [Oi^cra Logica, § iii., de Pro-
Ojjera, p. 345. Rensch, St/st. Log., -p. i2i. positionibus, c. xi. p. 487, and above,
Esser, LogiJc, § 58. Weiss, Logik, §§ 149, vol. i. p. 261.— Ed.]
150. So Kiesewetter, Logik, §§ 102, 103.]
282 APPENDIX.
But if we should convert the terms, the inadequacy would be
brouoht to li2;]it.
2°, A great number of notions are used principally, if not ex-
clusively, as attributes, and not as subjects. Men are, consequently,
very commonly ignorant of the proportion of the extension be-
tween the subjects and predicates, which they are in the habit of
combining into propositions.
3°, In regard to negatives, men naturally preferred to attribute
positively a part of one notion to another than to deny a part.
Hence the unfrequency of negatives with a particular predicate.
On the doctrine of Semi-definite Particularity, I would thus
evolve the Opposition or Incompossibility of propositions, neglect-
ing or throwing aside (with Aristotle) those of Subalternation
and Sub-contrariety, but introducing that oi Inconsistency.
Incompossibility is either of propositions of the same, or of dif-
ferent, quality. Incompossible propositions differing in quality are
either Contradictories without a mean, — no third, — that is, if one be
true the other must be false, and if one be false the other must be
true ; or Contraries with a mean, — a third, — that is, both may be
false, but both cannot be true. Incompossible propositions of the
same quality are Inconsistents, and, like Contraries, they have a
mean, that is, both may be false, but both cannot be true.
Contradictories are again either simple or complex. The simple
are either, 1", Of Universals, as undivided wholes; or, 2°, Of In-
dividuals, as indivisible parts. «
The complex are of universals divided, as 4 — 5.
Contraries, again, which are only of divided universals, are 1°,
Bilateral, as 1 — 5 ; or, 2°, Unilateral, as 1 — 6, 1 — 7, 2 — 5, 3 — 5 ;
or, 3", Cross, as 2—7, 3—6.
Inconsistents are either, 1°, Affirmatives ; or, 2°, Negatives. Af-
firmatives, as 1 — 2, 1 — 3, 2 — 3. Negatives, as 5 — 6, 5 — 7. The pro-
positions 6 — 7 are sometimes Inconsistents, sometimes Coosistents.
All the other propositional forms, whether of the same or of
different qualities, are Compossible or Unopposed.
The differences in Compossibility of the two schemes of Indefin-
ite and Definite particularity lies, 1°, in the whole Inconsistents ;
2°, in two Contraries for Contradictories. 1°, According to the
a General terms, used as individual Man is not mortal. So that there are
terms, when opposed to each other, may three kinds of conti'adictories.
be contradictories, as Man is mortal,
APPENDIX. 283
former, all affirmative and all negative propositions are consistent,
whereas in the latter these are inconsistent, ] — 2, 1 — 8, 2 — 3 ;
among the affirmatives, and among the negatives, 5 — 6, 5 — 7.
(As said before, 6 — 7 is in both schemes sometimes compossible,
and sometimes incompossible). 2°, Two incompossibles, to wit,
2 — 7, 3 — 6, which, on the Aristotelic doctrine, are Contradictories,
are in mine Contraries.
The propositional form 4 is consistent with all the affirmatives ;
8 is not only consistent with all the negatives, but is compossible
with every other form in universals. It is useful only to divide a
class, and is opposed only by the negation of divisibility.
By adopting exclusively the Indefinite particularity, logicians
threw away some important immediate inferences ; those, to wit, 1°,
From the affirmation of one some to the negation of another, and
vice versa; and, 2°, From the affirmation of one inconsistent to the
negation of another. 1°, Thus, on our system, but not on theirs,
affirming all man to he some animal, we have a right to infer that
no man is some {other) animal; affirming that some animal is all
man, we have a right to infer that some {other) animal is not any
man ; affirming some men are some blacks, {Negroes), we are en-
titled to say that {same) some men are not some {other ) blacks,
{Hindoos), and also that {other) some men are not the {same) some
blacks. And so backwards from negation to affirmation. This
inference I would call that of [Integration].
2°, Affirming all men ai^e some animals, we are entitled to
infer the denial of the propositions, all men are all animals, some
men are all animals. And so in the negative inconsistents.
Affieimatives.
1.) Toto-total = Afa = All — is all — .
ii.) Toto-partial = Afi = All — is some — . (A)
3.) Parti-total = Ifa = Some — is all — .
iv.) Parti-partial = Ifi = Some — is some — . (I)
Negatives.
V.) Toto-total — Ana = Any — is not any — . (E)
6.) Toto-partial = Ani = Any — is not some — .
vii.) Parti-total = Ina = Some — is not any — . (0)
8.) Parti-partial = Ini = Some — is not some — .
28 1
APPENDIX.
TABLE OF THE Mutual Relations of the Eight Propositional Forms
ON Either System of Particularity. (For Generals only.)
II.
Inverence
from Proposition to Proposition, ou the
two Systems.
2.
Definite Indeflni-
tude.
(Some at most.)
Restr. bi.
Restr, un.
Restr. un.
Restr. bi.
Restr. un.
Restr. un.
Res. & Int. bi.
Integr. un.
Res. & Int. un.
Integr. un.
Res. & Int. un.
Res. & Int. un.
Res. k Int. un.
Integr. bi.
1.
Indefinite Defini-
tude.
(Some at least.)
a d._; d a
3 3,^2 3 3
d d.A a d
3 3rQ 3 3
Restr
Restr
Restr
Restr
Restr
Restr
Restr
Restr
Restr
Restr
o
1— ii
1—3
1— iv
ii — iv
3-iv
V— 6
V — vii
V— 8
6-8
vii— 8
1-8
ii— 6
ii-8
3— vii
3-8
iv— 6, 6— iv
iv — vii, vii — iv
iv— 8, 8— iv
I.
Incompossibility
of Proposition with Proposition, on
the System of
Definite Indefini-
tude.
(Some at most.)
Incons. un.
Incons. un.
Incons. un. cr.
Incons. un.
Incons. un.
Doubtful cr.
Contrar. bi.
Contrar. un.
Contrar. un.
Contrar. un.
Contrar. bi. cr.
Contrar. un.
Contrar. bi. cr.
Contrar. bi. di.
1.
Indefinite Defini-
tude.
(So7ne at least.)
1
o
Q
Contrar. bi.
Contrar. un.
Contrar. un.
Contrar. un.
Rejjugn. bi. cr.
Contrar. un.
Repugn, bi. cr.
Repugn, bi. di.
Common to I. and II.,
iu either of which
all Propositions are related.
Of these their
"3
>
Mill!
1 1 1 1 II
rt c3 c3 ..-1 .1-1 _3
a a a a a 2
ol <- <j <J << »5
M M 1 1 1 1 1 1 1 1 1 1 II
:^:|:^:5^:^^:^;§^j|;|jajajaca
-73
'A
Afl5rmat.
1— ii
1—3
1-iv
ii-3
ii — iv
3— iv
Nea-at.
•M .« ti ._ .^ .M :3
'n'?CO'?GO0O^ >?o"?oo t»to'>ooioo'>oo t>«o >-Q0
1 1 1 II r. 1 1 1 1 1 1 II 1 II 1 M 1 1
> i> > CO to :a 5t) "-I "-I "-1 1-1 :S :a :a :a 50 CO CO CO >>,^>
Abbreviations: — hi. = lilateral ; cr. =: cross ; Contrar. = Contraries; A\. = direct ;
Incons. := Inconsistenis ; Int. or Integr. = Integration ; Repugn. = Repugnan.ts, Contra-
dictories ; Res. or Restr. = Restriction, Suhalter nation ; un. = unilateral. — Blanks: in I.
= Compossihles; in II. = No inference. — (Unilateral, bilateral, cross, direct, refer to the
Extremes. )
The preceding Table may not be quite accurate in details.
APPENDIX. 285
(e) SYLLOGISMS.
Observations on the Mutual Eelation of Syllogistic
Terms in Quantity and Quality.
General Canon. — What worst relation of subject and predicate,
subsists between either of two terms and a common third term,
with which one, at least, is positively related ; that relation
subsists between the tiuo terms themselves.
There are only three possible relations of Terms, (notions, repre-
sentations, presentations).
1°, The relation of Toto-total Coincliision, (coidentity, absolute
convertibility or reciprocation) (AfA).
2°, The relation of Toto-total Coexclusion, (non-identity, abso-
lute inconvertibility or non-reciprocation) (An A).
3°, The relation of Incomplete Coinclusion, which involves the
counter-relation of Incomplete Coexclusion, (partial identity and
non-identity, relative convertibility and non-convertibility, reci-
procation, and non-reciprocation). This is of various orders and
degrees.
a) Where the whole of one term and the part of another are
coinclusive or coidentical (Afl). This I call the relation of
toto-partial coinclusion, as All rtien are some animals. This
necessarily involves the counter-relation of toto-partial coexclu-
sion (AnI), as Any man is not some animal. But the con-
verse of this affirmative and negative affords the relations of
b) Parti-total Coinclusion ( IfA), and Coexclusion (InA), as
Somne animal is all man, Sonne anir)ial is not any man.
c) There is still a third double relation under this head, when
two terms partially include and partially exclude each other (If I
Inl), as Some ivomen are some authors, and Some women are
not some authors. This relation I call that of Parti-partial
Coinclusion, and Parti-partial Coexclusion.
Of these three general relations, the first is [technically styled]
the best ; the second is the worst ; and the third is intermediate.
Former logicians knew only of two worse relations, — a particular,
worse than a universal, affirmative, and a negative worse than an
affirmative. As to a better and worse in negatives, they knew
286
APPENDIX.
nothing ; for as two negative premises were inadmissible, they had
no occasion to determine which of two negatives was the worse or
better. But in quantifying the predicate, in connecting positive
and negative moods, and in generalising a one supreme canon of
syllogism, we are compelled to look further, to consider the inverse
procedures of affirmation and negation, and to show {e.g. in v. a.
and vi. b., ix. a. and x. b), how the latter, by reversing the former,
and turning the best quantity of affirmation into the worst of
negation, annuls all restriction, and thus apparently varies the
quantity of the conclusion. It thus becomes necessary to show
the whole order of best and worst quantification throughout the
two qualities, and how affirmation commences with the whole in
Inclusion and Negation, with the parts in Exclusion. «
Toto-total, ]
Toto-partial, I , .
-r, , . , , ) Identity or Comclusion.
Parti-total, | "^
Parti-partial. /
Parti-partial,^
Parti-total, I .
Toto-partial,
Non-identitvor Coexclusion.
Toto-total.
As the negation always reduces the best to the worst relation,
in the intermediate relations determining only a commutation from
equal to equal, whilst in both, the symbols of quantity, in their in-
verse signification, remain externally the same ; it is evident, that
the quantification of the conclusion will rarely be apparently diffe-
rent in the negative, from what it is in the corresponding positive,
mood. There are, indeed, only four differences to be found in the
negative from the positive conclusions, and these all proceed on the
same principle — viz. in v. a. and vi. b., in ix, a. and x. b. Here
the particular quantification of the positive conclusions disappears
in the negative moods. But this is in obedience to the general
canon of syllogism, — " that the worst relation subsisting between
either extreme and the middle, should subsist between the extremes
themselves." For what was the best relation in the former, becomes
the worst in the latter ; and as affirmation comes in from the
greatest whole, whilst negation goes out from the least part, so, in
point of fact, the some of the one may become the not any of the
a See Magentinus, (in Brandis, Scholia, p. 113, and there the Platonics.)
APPENDIX.
287
other. There is here, therefore, manifestly no exception. On the
contrary this affords a striking example of the universal applicabi-
lity of the canon under every change of circumstances. The canon
would, in fact, have been invalidated, had the apparent anomaly
not emero;ed.
I. Terms each totally coinclu-
sive of a third, are totally co-
inclusive of each other.
II. Terms each parti- totally
coinclusive of a third, are parti-
ally coinclusive of each other.
III. A term totally, and a
term parti-totally, coinclusive of
a third, are toto-partially coin-
clusive of each other.
IV. A term parti-totally, and
a term totally, coinclusive of a
third, are j)arti-totally coinclu-
sive of each other.
V. A term totally, and a term
toto-partially, coinclusive of a
a) A term totally coexclu-
sive, and a term totally coin-
clusive, of a third, are totally
eoexclusive of each other.
b) A term totally coinclu-
sive, and a term totally eoex-
clusive, of a third, are totally
eoexclusive of each other.
a) A term parti-totally co-
exclusive, and a term parti-totally
coinclusive, of a third, are parti-
ally eoexclusive of each other.
b) A term parti-totally coin-
clusive, and a term parti-totally
eoexclusive, of a third, are par-
tially eoexclusive of each other.
a) A terra totally eoexclusive,
and a term parti-totally coin-
clusive, of a third, are toto-parti-
ally eoexclusive of each other.
b) A term totally coinclusive,
and a term parti-totally eoexclu-
sive, of a third, are toto-j)artially
eoexclusive of each other.
a) A term parti-totally co-
exclusive, and a term totally co-
inclusive, of a third, are joarti-
totally eoexclusive of each other.
b) A term parti-totally co-
inclusive, and a term totally co-
exclusive, of a third, are jjarti-
totally eoexclusive of each other.
a) A term totally eoexclusive,
and a term toto-partially coin-
288
APPENDIX.
third, are parti-totally coinclu-
sive of each other.
VI. A term toto - partially,
and a term totally, coiiicliisive
of a tliird, are toto -partially
coiiiclusive of each other.
VII. A term parti-totally, and
a term partially, coinclusive of a
third, are partially coinclusive
of each other.
VIII. A terra partially, and a
term parti-totally, coinclusive of
a third, are partially coinclusive
of each other.
IX. A term totally, and a
term partially, coinclusive of a
third, are partially coinclusive of
each other.
X. A term partially, and a
term totally, coinclusive of a
elusive, of a third, are totally
coexclusive of each other.
b) A term totally coinclusive,
and a term toto-partially coex-
clusive, of a third, are parti-totally
coexclusive of each other.
a) A term toto-partially co-
exclusive, and a term totally co-
inclusive, of a third, are toto-par-
tially coexclusive of each other.
b) A term toto-partially co-
inclusive, and a term totally co-
exclusive, of a third, are totally
coexclusive of each other.
a) A term parti-totally co-
exclusive, and a term partially
coinclusive, of a third, are parti-
ally coexclusive of each other.
b) A term parti-totally co-
inclusive, and a term jjartially
coexclusive, of a third, are par-
tially coexclusive of each other.
a) A term partially coexclu-
sive, and a term parti-totally co-
inclusive, of a third, are partially
coexclusive of each other.
b) A term partially coinclu-
sive, and a term parti-totally co-
exclusive, of a third, are partially
coexclusive of each other.
a) A term, totally coexclusive,
and a term partially coinclusive,
of a third, are parti-totally co-
exclusive of each other.
b) A term totally coinclusive,
and a term jiartially, coexclusive
of a third, are partially coexclu-
sive of each other.
a) A term partially coexclu-
sive, and a term totally coinclu-
APPENDIX.
289
third, are partially coiucliisive of
each other.
XI. A term parti-totally, and
a term toto-partially, coinclusive
of a third, are parti-totally co-
inclusive of each other.
XII. A term toto-partially,
and a term parti-totally, coinclu-
sive of a third, are toto-partially
coinclusive of each other.
sive of a third, are partially co-
exclusive of each other.
b) A term partially coinclu-
sive, and a term totally coexclu-
sive, of a thii'd, are toto-partially
coexclusive of each other.
a) A term parti-totally coex-
clusive, and a term toto-parti-
ally coinclusive, of a third, are
parti-totally coexclusive of each
other.
b) A term parti-totally coin-
clusive, and a term toto-partially
coexclusive, of a third, are parti-
totaUy coexclusive of each other.
a) A term toto-partially coex-
clusive, and a term parti-totally
coinclusive, of a third, are toto-
partiaUy coexclusive of each
other.
b) A term toto-partially co-
inclusive, and a term parti-totally
coexclusive, of a third, are toto-
partially coexclusive of each
other.
(y).__OBJECTIONS TO THE DOCTRINE OF A QUANTIFIED
PREDICATE CONSIDERED.
(I). Geneeal.
MATERIAL AND FOEMAL.— THEIR DISTINCTION.
But it is requisite, seeing that there are such misconceptions
prevalent on the point, to determine precisely, what is the formal
which lies within the jurisdiction of Logic, and which Logic gua-
rantees, and what the material which lies without the domain of
Logic, and for which Logic is not responsible. This is fortunately
easy.
VOL. II. T
290 APPENDIX.
Logic knows, — takes cognisance of, certain general relations ;
and from these it infers certain others. These and these alone it
knows and guarantees ; and these are formal. Of all beyond these
forms or general relations it takes no cognisance, affords no assur-
ance ; and only hypotlietically says, — If the several notions applied
to these forms stand to each other in the relation of these forms,
then so and so is the result. But whether these notions are rightly
applied, that is, do or do not bear a certain reciprocal dependence,
of this Logic, as Logic, knows nothing. Let ABC represent three
notions, A containing B, and B containino; C ; in that case Logic
assures us that C is a part of B, and B a part of A ; that A contains
C ; that C is a part of B and A. Now all is formal, the letter:
being supposed to be mere abstract symbols. But if we apply to
them, — fill them up by, — the three determinate notions,— iL?u'maZ
— 3Ian — Negro, we introduce a certain "inatter, of which Logic is
not itself cognisant ; Logic, therefore, merely says, — If these notions
hold to each other the relations represented by A B C, then the
same results will follow ; but whether they do mutually hold these
relations, — that, as material, is extra-logical. Logic is, therefore,
bound to exhibit a scheme of the forms, that is, of the relations in
their immediate and mediate results, which are determined by the
mere necessities of thinking, — by the laws of thought as thought ;
but it is bound to nought beyond this. That, as material, is beyond
its jurisdiction. However manifest, this has, however, been fre-
quently misunderstood, and the material has been currently passed
off in Logic as the formal.
But further. Logic is bound to exhibit this scheme full and un-
exclusive. To loj) or limit this in conformity to any circumstance
extrinsic to the bare conditions, — the mere form, of thought, is a
material, and, consequently, an illegitimate curtailment. To take,
for instance, the aberrations of common language as a model,
would be at once absurd in itself, and absurd as inconsistent even
with its own practice. And yet this double absurdity the Logic
now realised actually commits. For while in principle it avows
its allegiance to thought alone ; and in part it has overtly repudi-
ated the elisions of language ; in part it has accommodated itself
to the usages of speech, and this also to the extent from which even
Grammar has maintained its freedom. Grammar, the science pro-
per, — the nomology, of language, has not established ellipsis as a
APPENDIX. 291
thii'd law beside Concord and Government ; nor lias it even allowed
Concord or Government to be superseded by ellipsis. And why ?
Because the law, though not externally expressed in language, was
still internally operative in thought. Logic, on the contrary, the
science proper, — the nomology, of thought, has established an im-
perative ellipsis of its abstract forms in conformity to the precari-
ous ellipses of outward speech ; and this, although it professes to
look exclusively to the internal process, and to explicate, — to fill
up what is implied, but not stated, in the short cuts of ordinary
language. Logic has neglected, — withheld, — in fact openly sup-
pressed, one-half of its forms, (the quantification of the predicate
universally in afiirmatives, particularly in negatives), because
these forms, though always operative in thought, were usually
passed over as superfluous in the matter of expression.
Thus has logic, the science of the form, been made hitherto the
slave of the matter, of thought, both in what it has received and in
what it has rejected. And well has it been punished in its servi-
tude. More than half its value has at once been lost, confusion
on the one hand, imperfection on the other, its lot ; disgust, con-
tempt, comparative neglect, the consequence. To reform Logic,
we must, therefore, restore it to freedom ; — emancipate the form
from the matter ; — we must, I'', Admit nothing material under
the name of formal, and, 2°, Reject nothing formal under the
name of material. When this is done, Logic, stripped of its acci-
dental deformity, walks forth in native beauty, simple and com-
plete ; easy at once and useful.
It now remains to show that the quantities of the Predicate de-
nounced by logicians are true logical forms.
-s * * -X- * *
The logicians have taken a distinction, on which they have de-
fended the Aristotelic prohibition of an overt quantification of the
predicate ; the distinction, to wit, of the formal, in opposition to
the material, — of what proceeds vi formce, in contrast to what
proceeds vi materia. It will be requisite to determine explicitly
the meaning and application of these expressions ; for every
logical process is formal, and if the logicians be correct in what
they include under their category of material, the whole system
which I would propose in supplement and correction of theirs,
must be at once surrendered as imtenable.
292 APPENDIX.
In the first place, the distinction is not estahlished, in terms at
least, by Aristotle. On the contrary, although the propositional
and syllogistic relations which he recognises in his logical precept
be all formal, he, as indeed all others, not unfrequently employs
some which are only valid, say the logicians, vi materice, and not
ratione formce^ that is, in spite of Logic.
But here it is admitted, that a distinction there truly us ; it is,
consequently, only necessary, in the second place, to ascertain its
import. What then is meant by these several principles ?
The answer is easy, peremptory, and unambiguous. All that is
formal, is true as consciously necessitated by the laws of thought ;
all that is material, is true, not as necessitated by the laws of
thought, but as legitimated by the conditions and probabilities dis-
coverable in the objects about which we chance to think. The one
is a priori, the other a posteriori ; the one is necessary, the other
contingent ; the one is known or thought, the other unknown or
unthought.
Por example ; if I think that the notion triangle contains the
notion trilateral, and again that the notion trilateral contains the
notion triangle; in other words, if I think that each of these is
inclusively and exclusively applicable to the other ; I formally say,
and, if I speak as I think, must say — All triangle is all trilateral.
On the other hand, — if I only think that all triangles are trilateral,
but do not think all trilaterals to be triangular, and yet say, — All
triangle is all trilateral, the proposition, though materially true,
is formally false.
Again, if I think, that this, that, and the other iron-attracting
stones are some magnets, and yet thereon overtly infer, — All
magnets attract iron ; the inference is formally false, even though
materially not untrue. Whereas, if I think that this, that, and the
other iron-attractijig stones are all magnets, and thence conclude, —
All magnets attract iron ; my conclusion is formally true, even
should it materially prove false.
To give the former example in an abstract notation : If I note
C : B1 IIII : r, I may formally convert the proposition and state
Y : teaa» — : C. But if I note C : b»- — r, I cannot formally
convert it ; for the F niay mean either : r or > F ; and if I do,
the product may or may not be true according as it is accidentally
APPENDIX. 293
applied to this or that particular matter. As to the latter ex-
ample : C, ■■ » : (m m' m," &c.) :- : r
This syllogism is formally legitimate. But, to take the following
antecedent : this, if formally drawn, warrants only, (1), a particular
conclusion ; and if, (2), a universal be drawn, such is logically null :
C, »■ : (m m' m" &c.) : wb, r
This being the distinction of formal and material, — that what
is formally true, is true by a subjective or logical law ; — that what
is materially true, is true on an objective or extra-logical condition ;
the logicians, with Aristotle at their head, are exposed to a double
accusation of the gravest character. For they are charged : — 1°,
Tliat they have excluded, as material, much that is purely formal ;
2°, That they have included, as formal, much that is purely material.
Of these in their order.
1°, I shall treat of this under the heads of Affirmative and of
Negative propositions.
Of the four Affirmative relations of concepts, as subject and
predicate ; to wit — 1, The Toto-total ; 2, The Toto-partial ; 3, The
Parti-Total ; 4, The Parti-Partial ; one half (1, 3) are arbitrarily
excluded from logic. These are, however, relations equally neces-
sary, and equally obtrusive in thought, with the others ; and, as
formal realities, equally demand a logical statement and considera-
tion. Nay, in this partial proceeding, logicians are not even self-
consistent. They allow, for example, the toto-jyartial dependency
of notions, and they allow of their conversion. Yet though the
terms, when converted, retain, and must retain, their original re-
lation, that is, their reciprocal quantities ; we find the logicians,
after Aristotle, declaring that the predicate in affirmative proposi-
tions is to be regarded as particular ; howbeit, in this instance,
where the toto-partial is converted into the parti-total relation,
theu' rule is manifestly false. When I enounce, — All man is
animal, I mean, — and the logicians do not gainsay me, — All man
is some animal. I then convert this, and am allowed to say, —
o For an exjilanation of the notation gism, see below, Appendix XI, — Ed,
here employed, in reference to Syllo-
294 APPENDIX.
So)ne animal is man. But I am not allowed to say, in words,
though 1 say, — indeed must say, in thought, — Some animal is
all man. And why ? Simply because there is an old traditionary
rule in Logic, which j^rohibits us in all cases, at least of affirmative
pro230sitions, to quantify the predicate universally ; and to estab-
lish a reason for this exclusion, the principle of materiality has
been called in. But if all is formal which is necessitated by thought,
and if all that is formal ought to find an expression in Logic, in
that case, the universal quantification of the notion, when it stands
as predicate, may be, ought, indeed, on demand, to be, enounced,
no less exjilicitly than when it stood as subject. This quantifica-
tion is no more material on the one alternative than on the other ;
it is formal in both.
In like manner, the toto-total relation is denounced. But a
similar exposition shows that notions, thought as reciprocating or
coequal, are entitled, as predicate, to have a universal quantifica-
tion, no less than as subject, and this formally, not materially."
Li regard to the four Negative relations of terms, — 1. The Toto-
total,— 2. The Toto-partial,—'^. The Parti-total,— k The Parti-
partial; in like manner, one half, but these wholly different
classes, (3, 4), are capriciously abolished. I say capriciously ; for
the relations not recognised in Logic are equally real in thought,
as those which are exclusively admitted. Why, for example, may
I say, as I think, — Some animal is not any man ; and yet not
say, convertibly, as I still think, — Any man is not some animal?
Por this no reason, beyond the caprice of logicians, and the elisions
of common language, can be assigned. Neither can it be shown,
as I may legitimately think, — Some animal is not some animal,
(to take an extreme instance), that I may not formally exjiress the
same in the technical language of reasoning.
In these cases, to say nothing of others, the logicians have,
therefore, been guilty of extruding from their science much that
is purely formal ; and this on the untenable plea, that what is
formal is material.
a. It is hardly requisite to notice the ojnnion is explicitly renounced by the
blundering doctrine of some authors, acuter logicians, when they have chanced
that the predicate is materially quantified, to notice the absurdity. — See Fonseca,
even when predesignated as universal. Instit. Dial. 1. vi., c. 20.
It is sufBcient to observe that this
APPENDIX. 295
(2). Special.
Two objections have been taken to the universal quantification
of the predicate. It is said to be— 1°, False; 2°, If not false,
useless.
I. The first objection may be subdivided into two heads, inasmuch
as it may be attempted to establish it, a), on material ; b), on
formal, grounds. Of these in their order : —
a). This ground seems to be the only one taken by Aristotle,
who, on three (perhaps on four) different occasions denounces the
universal quantification of the predicate (and he but implicitly
limits it to affirmative propositions), as " aliuays untrue^"- The
only 23roof of this imexclusive denunciation is, however, one special
example which he gives of the falsity emerging in the proposition,
— All man is all animal. This must be at once confessed false ;
but it is only so materially and contingently, — argues, therefore,
nothing for the formal and necessary illegitimacy of such a quanti-
fication. As extra-logical, this proof is logically incompetent ; for
it is only because we happen, through an external knowledge, to
be aware of the relations of the concepts, man and animal, that
the example is of any import. But, because the universal quanti-
fication of the predicate is, in this instance, materially false, is such
quantification, therefore, always formally illegal ? That this is not
the case, let us take other material examj)les. Is it, then, materially
false and formally incompetent, to think and say, — All human is
all rational, — All rational is all risible, — All risible is all capa-
ble of admiration, — All trilateral is all triangular, — All trian-
gular is all figure with its angles equal to turn right angles, &c. ?
Or, employing Aristotle's material example, is it untrue, as he
asserts, to say — Some animal is all man ; and this either collec-
tively, — A part of the class animal is the whole of the class man,
— or distributivehj, — Some several animal is every several man.
But the absurdity of such a reasoning is further shown by the
fact, that if it were cogent at all, it would equally conclude against
the validity of the universal quantification of the subject. For
this proposition is equally untrue (employing always Aristotle's
own material example), — All animal is man.
After this, it may the less surprise us to find that Aristotle
« See below, p, 298.— Ed.
296 APPENDIX.
silently abandons liis logical canon, and adheres to truth and nature.
In fact, he frequently does in practice virtually quantify the predi-
cate, his common reasonings often proceeding on the reciprocation
or coextension of subject and predicate. Nay, in his logical
system, he expressly recognises this coextension ; unless, indeed,
we overtly supply the quantification of the predicate, his doctrines
of Induction and of Demonstration proper have no logical nota-
tion ; and, unless we covertly suppose it, they are actually arrested.
His definitions of the Universal, as severally given in his Prior
and Posterior Analytics, are, in this respect, conflictive. In the
former, his universal, (known in the schools as the Universale
Prioristicum), explicitly forbids, whereas the latter, (the Univer-
sale Posterioristicum of the schoolmen), implicitly postulates, the
quantification of the predicate.
b). The defect in the polemic of their master was felt by his
followers. They, accordingly, in addition to, but with no correc-
tion of, Aristotle's doctrine, argue the question on broader ground ;
and think that they disjirove the formal validity of such quantifi-
cation by the following reasoning. Overlooking the case, where
the subject is particularly, the predicate universally, quantified, as
in the instance I have just given, they allege the case of what are
called reciprocatiiig propositions, where both subject and predicate
are taken in their utmost extension, vi materiw, as subsequent
logicians " say, but not Aristotle. In this case, then, as in the
example. All man is all risible, they assert that the overt quanti-
fication of the predicate is inept, because, the all as applied to
the subject being distributively taken, every individual man, as
Socrates, Plato, &c., would be all, (that is, the whole class), risible.
This objection is only respectable by authority, through the great,
the all but unexclusive, number of its allegers ; in itself it is futile.
Terms and their quantifications are used either in a distributive,
or in a collective, sense. It will not be asserted that any quantifi-
cation is, per se, necessarily collective or necessarily distributive ;
and it remains to ascertain, by rule and relation, in which signi-
fication it is, or may be, employed. Now a general rule or postu-
late of logic is, — That in the same logical unity, (jDroposition or
syllogism), the same term or quantification should not be changed
a, [See, for example, Pacius, In An. In An. Prior, L. i., c. 9, and above, p.
Prior, L. i., c. 5, p. 134. Alexander, 274, note a, sm5. /».]
APPENDIX. 297
in import.a If, therefore, we insist, as insist we ouglit, that the
quantification here, all, should be used in the same proposition
ill the same meaning, that is, as applied to the one term, collec-
tively or distributively, it should be so applied likewise to the
other, the objection fails. Thus taken collectively: — All, (that
is, the whole class), man is all, (that is, the whole class), risible,
the projiosition is valid. Again, taken distributively : — All, (that
is, every several), man is all, (that is, every several), risible, the
proposition is, in like manner, legitimate. It is only by violating
the postulate, — That in the same logical unity ^ the same sign or
luord should be used in the same sense, that the objection applies ;
whereas, if the postulate be obeyed, the objection is seen to be
absurd.
It is hardly necessary to say anything in confutation of the
general doctrine, that in Reciprocating propositions the predicate is
taken in its full extent, vi materice. In the first place, this doc-
trine was not promulgated by Aristotle ; who frequently allowing, —
frequently using, — such propositions, implicitly abandons the rule
which he explicitly lays down in regard to the non-predesignation
of the predicate by a imiversal. In the second place, apart from
authority, such doctrine is in itself unfounded. Por as form is
merely the necessity of thought, it is as easy to think two notions
as toto-totally coinciding, (say, triangle and trilateral), as two
notions toto-j)artially and parti-totally coincidmg, (say, triangle
and figure). Accordingly, we can equally abstractly represent their
relations both by geometric quantities, (lines or figures), and by
purely logical symbols. Taking lines : — the former i ; the
latter I . Taking the symbols, the former C : i— : F ;
the latter A, esb=— — : B. But if the reciprocation were deter-
mined by the mere matter, by the object contingently thought
about, all abstract representation would be impossible. So much
for the first objection, — that the universal quantification of the
predicate would, at least in afiirmative propositions, be false.
II. As to the second objection, that such quantification would
be useless and superfluous, disorderly, nay confusive, this only
manifests the limited and one-sided view of the objectors, even
though Aristotle be at their head.
* See above, p. 253. — Ed.
298 APPENDIX.
Is it useless in any case, theoretical or practical, that error be
refuted, truth established ? And in this case : —
1°, Is it disorderly and confusive, that the doctrine of Expon-
ihles, as they are called, should be brought back from anomaly
and pain to ease and order, — that propositions Exclusive and
Exceptive, now passed over for their difficulty, and heretofore
confessedly studied as " opprobria and excruciations," should be
shown to be, not merely reducible by a twofold and threefold tor-
tuosity, through eight genera and eight rules, but simple, though
misunderstood, manifestations of the universal quantification of
the predicate ? ""
2", Is it useless to demonstrate that every kind of proposition
may be converted, and not some only, as maintained by Aristotle
and the logicians? And is it disorderly and confusive, in all
cases, to abolish the triple (or quadruple) confusion in the triple
(or quadruple) j)rocesses of Conversion, and to show, that of these
processes there is only one legitimate, and that, the one simple of
the whole ?
3°, Is it disorderly and confusive to abolish the complex confu-
sion of Mood and Figure, with all their array of rules and excep-
tions, general and special ; and thus to recall the science of reason-
ing to its real unity ?
4°, Is it useless and superfluous to restore to the science the
many forms of reasoning which had erroneously, inefi'ectually, and
even inconsistently, been proscribed ?
5°, Is it useless or sujierfluous to prove, that all judgment, and,
consequently, all reasoning, is simply an equation of its terms, and
that the diflerence of subject and predicate is merely arbitrary ?
6°, In fine, and in sum, is it useless or siq^erfluous to vindicate
Logic against the one-sided views and errors of logicians, to recon-
cile the science with truth and nature, and to reestablish it, at
once, in its amplitude and simplicity ?
{g) — HisTOEicAL Notices of Doctkine of
Quantified Peedicate.
I. — Afjstotle.
It will be sufficient to make one extract from Aristotle in illus-
o See above, p. 2C1. — Ed.
APPENDIX. 299
tration of his doctrine upon this point, and I select the following
passage from his Categories, c. v. § 7-
" Further, the primary substances, [Trpwrat ovcriai, — individual
existences], — because they are subjects to all the others, and as all
the others are predicated of, or exist in, them, — are, for this reason,
called substances by pre-eminence. And as the primary sub-
stances stand to all the others, so stands the Species to the Genus.
For genera are predicated of species, hut not, conversely, species
of genera; so that of these two, the species is more a substance
than the genus."
Ammonius, who has nothing in his Commentary on the Cate-
gories relative to the above passage of Aristotle, states, however,
the common doctrine, with its reasons, in the following extract
from his Conmientary on Porphyry's Introduction, (£ 29, ed. Aid.
1546).
" But confining ourselves to a logical consideration, it behoves
us to inquire, — of these, which are subjected to, which predicated
of, the others ; and to be aware, that Genera are predicated of
Differences and Species, but not conversely. These, as we have
said, stand in a certain mutual order, — the genus, the difference,
and the species ; the genus first, the species last, the difference in
the middle. And the superior must be predicated of the inferior ;
for to jDredicate the inferior of the superior is not allowable. If,
for examj)le, we say, — All man is animal, the proposition is true ;
but if we convert it, and say, — All animal is man, the enounce-
nient is false." Again, if we say, — All horse is irrational, we are
right ; but if conversely we say, — All irrational is horse, we are
wrong. For it is not allowed us to make a subject of ^the acci-
dental. Hence is it incompetent to say that Animal is man, as
previously stated."
[Categ. ch. ii. § 1.
" When one thing is predicated of another as of its subject, all
that is said [truly] of the predicate will be said [truly] also of
a The converse of a true proposition animal, and, All horse is some irra-
is always truej but the false proposi- tional. Convert these, — Some animal
tions which are here given, as conver- is all man, and, So)ne irrational is all
sions of the true, are not conversions horse; the truth remains, but the one-
at all. The true propositions, if ex- sided doctrine of the logicians is ex-
plicitly stated, are, — All man is some ploded.
800 APPENDIX.
the subject. Thus man is predicated of this and that man,'^ and
animal of man ; animal will therefore be predicated of this and
that individual, for this and that individual is both man and
animal."
De Interpret, c. vii. § 2-4. ; see also c. x.
" To enounce something of a universal universally, I mean as,
All or every man is white, No man is white
To enounce something of universals not universally, I mean as,
Man is white, Man is not ivhite ; for whilst the term man
is universal, it is not used in these enouncements as universal.
For all or every (770,9) does not indicate the universal [itself],
but that [it is applied to a subject] universally. Thus, in
reference to an universal predicate, to predicate the universal, is
not true. Por no affirmation is true, in which the universal is
predicated [of an universal predicate], as, All or every man is all
or every animal." (See Ammonius, Boethius, Psellus, Magentinus,
&c).
Prior Analytics, Bk. I. c. 27, §. 9. "The consequent [i.e. the
predicate] is not to be taken as if it wholly followed [from the
antecedent, or subject, exclusively]. I mean, for example, as if
all [or every'] animal [were consequent] on man, or all [or every^
science on m,usic. The consequence simply [is to be assumed], as
in our propositions has been done ; to do otherwise (as to say that
all [or every] man is all [or every] animal, or that justice is
all [or every] good, is useless and impossible ; but to the antece-
dent [or subject] the all or [every] is prefixed."
Posterior analytics, B. I. c. xii. § 10. "The predicate is not
called all [or every ] ; [that is, the mark of universality is not
annexed except to the subject of a proposition].
In refutation of Aristotle's reasoning against the universal j^re-
designation of the predicate — it will equally disprove the universal
predesignation of the subject. For it is absurd and impossible to
say, All animal is man; All (every) immortal is the soul;
All 2}leasure is health; All science is music; All motion is
pleasure.^ But in point of fact such examples disprove nothing ;
f(jr all universal predesignations are applicable neither to subject
a. [For the rh here, as el.sewhere, de- )3 Examples from Wegelin, In Grcj.
notes the indlviduum signatum, not the Aneponymi Comp. Phil. Sijnt. L. iv. c.
indlviduum vagum.] 1, p. 473; L. vi. c. 1, p. G73.
APPENDIX.
301
nor predicate, nor to both subject and predicate — are thoughts not
things; and so are all 2^redesignations ; therefore, &c. It is only
marvellous that such examples and such reasoning could satisfy the
acutest of intellects ; that his authority should have imposed on
subsequent logicians is less wonderful a]
Quantification of Predicate — Aristotle.
1. Admits that syllogism mental not oral (An. Post. I. 10). This
to be borne in mind.
2. That individual is never predicated, (Cat. c. 2), refuted by re-
ciprocation of singular, (An. Pr\ ii. 23, § 4).
3. That affirmative universal not [to] be added to predicate, incom-
patible with what he says of reciprocation, (in An. Pr. ii. cc.
22 and 23 alibi). That his custom to draw universal conclu-
a And here I may correct an error, as
I conceive it to be, which has descended
fi'om the oldest to the most recent in-
terpreters of the Organon, and been
adopted implicitly by logicians in gene-
ral. It is found in Alexander and
Ammonius, as in Trendelenburg, Saint-
Hilaire, and Waitz ; nor indeed, as far
as I know, has it ever been called in
question during the interval. It regards
the meaning of the definition elevated
into a two-fold axiom, the esse in toto,
&c., and did de omni, &c., toward the
conclusion of the first chapter of the
first book of the Prio7' Analytics. 1h Se
(V o\(f! elvai fT€pov erepaj Kol rh Kara
■wayTos KaTrjyopeladaL OaT^povdarepourav-
t6v icrriv. This, with its ambiguity, may
be thus literally, however awkwardly,
translated : — " But [to say] that one
thing is in a whole other, and [to say]
that one thing is predicated of all an-
other, are identical." — Now, the question
arises, — What does Aristotle here mean
by " a whole other V for it may signify,
either the class or higher notion under
which an inferior concept comes, or the
inferior concept itself, of which, as of a
subject, the higher is predicated. The
former is the sense given by all the
commentators; the latter, the sense
which, I am confident, was intended by
Aristotle.
There are only two grounds of inter-
pretation. The rule must be expounded
in consistency — 1°, "With itself ; 2°, Must
be with the analogy of Aristotelic usage.
1°. On the former ground, the com-
mon doctrine seems untenable; for what
Aristotle declares to be identical, by that
doctrine becomes difi'erent, nay ojiposed.
An inferior concept may be in a higher
whole or class, either partially or totallj' ;
and the definition on the prevalent in-
terpretation virtually runs — " To say
that one thing is all or ^Mrt in the whole
of another, and to say that this other
is predicated of it unexclusively, are
convertible." Had Aristotle, therefore,
used the expression in the signification
attributed to him, he must, to avoid the
contradiction, have said — T^ Se izav
erepoy iv oXc^ elvai ^repcp k.t.A. (" But
to say that one thing is all in a whole
other," &c.)
2°. On the second ground, it may,
however, be answered, that the ambi-
guity of the word, as it stands, is super-
seded, its signification being determined
by other passages. I join issue ; and on
this ground am well content to let the
question be decided.
302
APPENDIX.
sions in Thiixl Figure and affirmative in Second'' with allow-
ance of simple conversion in certain universal affirmatives.
That particular not in negative predicate, absurd in ov Tras,
non omnis.
Aristotle's doctrine of Predesignation.
1°, How can Aristotle, on his doctrine, make universal terms taken
indifferently, or without predesignation, be tantamount to parti-
culars? {An. Prior, I. c. 4, § 13, Org. Pacii, p. 135, alibi),
2°, An. Prior, 1, c. 27, § 7. He says, as elsewhere, " a proposi-
tion being indefinite, [preiu designate], it is not clear whether it be
universal ; when, however, it is definite, [predesignate], that is
manifest." Contrast this statement with his doctrine of the all.
3°, There are syllogisms in Aristotle, which are only valid
through the quantity of the predicate./^
4°, Aristotle requires, though he does not admit, the universal
In the first place, the meaning I attri-
bute to the expression, " wlwle other " — -
that is, whole subject or inferior notion,
is, in short, in strict conformity with
Aristotle's ordinary language. There
are, I admit, sundry passages in his logi-
cal writings, where the term whole is
clearly used as synonymous with class
or higher notion ; as, to limit ourselves
to the Prior Analytics, in Book I. iv., §
2 ; and II. i. § 4. But, every single text,
in which the term whole appears in this
relation, is overruled by viore than five
others, in which it is no less clearly ap-
plied to denote the totality of a lower
notion, of which a higher is predicated —
passages in which the word whole (ciAos)
is used convertibly with all (ttSs). See
for example, A n. Pr. II. ii., § 5, § 1 6 — iii.
§ 5, § 7 {his.), § 13 [his.], § 14, § 15-iv. §
6 {bis.), § 8, § 10, § 12 (iM.)— xxii. § 7, §
8 — xxiii. § 4.
But in the second place, (and this is
directly subversive of the counter-opi-
nion, even in the principal of the few
passages where the term ivhole is used
for class), the lower notion may be in
or under the higher, only 2Mrticularly ;
and this manifestly shows that Aristotle
c<juld not possibly mean, by merely
saying, that one thing is another, as in a
class, that it is so unexclusively, or uni-
versally. Compare An. Pr. I. iv. §§ 2,
3, 1 0. On this interpretation, Darii and
Ferio would then be annulled ; a special
result which ought to have startled the
logicians into a doubt of the accuracy
of the received doctrine in general. (See,
instar omnium, Pacius, in his relative
Notes and Commentary.)
That doctrine must, therefore, be aban-
doned, and the rule reduced to a defini-
tion, read in the following signification :
— " But to say that one thing is in the
whole of another, as in a subject, and to
predicate one thing universally of another,
are merely various expressions of the
same meaning." This, in fact, is just
the preliminary explanation of the two
oi'dinary modes of stating a proposition,
subsequently used by Aristotle. Here,in
both convertibles, he descends from ex-
tension to comprehension, from the pre-
dicate to the subject; and the ingenious
exposition by the commentators, old and
new, of the inverse intention of the phi-
losopher in the two clauses, must be re-
garded as erroneous.
a See below, p. 346. — Ed.
/8 See below, p. 346.— Ed.
APPENDIX. 803
predesignatioii of the predicate in his syllogism of Induction. Vide
An. Prior., L, ii., c. 23, § 4, Organon Pacii, p. 399. Compare
also his doctrine, p. 396.)
II. Alexandek Aphrodtsiensis.
Alexander Aphrodisiensis, in his commentary on the first book
of the Prior Analytics, and in reference to the second passage of
Aristotle, states as follows :
"And in the book of Enouncement Aiistotle explains, why he
there says : — ' that to predicate the universal of a universal predi-
cate is not true ; for there will be no proposition, if in it we pre-
dicate the universal of the universal, as, All man is all animal.'
He repeats the same also here ; showing, how it is useless to
attempt thus to express the consecution, [of higher from lower
notions] ; and adds, that it is not only useless, but impossible.
For it is impossible, that all man should be all animal, as
\_useless to say, {a)(pr)(TTOv eiireiv must have dropt out)], that all
man is all risible. We must not, therefore, apply the all to the
consequent, [or predicate], but to that from which it follows, [or
subject]. For man is to be taken universally, as that from which
animal follows, supposing this to be the consequent of all man.
Thus shall we obtain a stock of universal jiropositions. The process
is the same, in making man the consequent on its proper all;
but man is not consequent on all biped, but on all rational.
" The words, ' as we express ourselves,' mean — as we express
ourselves in common usage. For we say, that all man is simply,
animal, and not all animal, and that all pleasure is natural, not
all natural; prefixing the all, not to the consequent, but to the
subject from which the predicate follows." {Edd. Aid., f. 100 a;
Junt., f. 122 a ; Compare Aid., f. 86 a ; Junt, f. 105 a.)
III. — Ammonius Heemi.e.
Ammonius Hermife, In de Tnterp. c. vii. § 2. (Aldine edi-
tions, of 1503, sig. C. vii. 59, of 1546, ff. 70, 74).
" In these words Aiistotle inquires : — Whether, as the an-
nexation of the affirmative predesignation (TTjOocrStoptcr/xo?) to the
304 APPENDIX.
subject constitutes one distinct class of propositions, the same
annexation to the predicate, may not, likewise, constitute another ;
and he answers, that the supposition is absolutely groundless.
Thus the enouncement — all (or every) man is all (or every) ani-
7nal, (tto,? dvOpcoTTOs ttou Ifiiov ecm) ; asserts that each man is
all animal — as horse, ox, &c. But this proposition is impos-
sible ; as is shown by Aristotle in his here omitting the word
' true.' For no affirmation can be true, in which the universal is
predicated of a universal predicate ; that is, in which the universal
predesignate is added to a universal predicate ; as when we say
that man (of whom all, or, as he says, universally, animal is
predicated), is not simply animal, but all animal. He, therefore,
teaches, that such an affirmation, as utterly untrue, is utterly in-
competent
" Neither does Aristotle allow the predesignation some to be
annexed to the predicate, that propositions may, thereby, become
true always or occasionally. For logicians, (as they do not pro-
]DOse to themselves every superfluous variety of enunciation), are
prohibited from considering propositions, (not only those always
true or always false), but those which express no difference in re-
ference to necessary or impossible matter, and afford us absolutely
no discrimination of truth from falsehood. Thus, particular pro-
positions, which may be alternatively true and false, ought not to
have a predesignated predicate. For in a proposition, which has
all their power, without any predesignation of its predicate ; why
should we prefer to the simpler expression, that which drags about
with it a superfluous additament ? Why, for example, instead of —
All man is some animal, [I read, tl ^(oov], or. All man is not all
animal,"" should we not say — All man is animal, and in place of
All man is no stone, not say, — All man is not stone ; or, what
is a simpler and more natural enouncement still, — Ko man is stone.
"And when we find some of the aiicients teaching that the
particular affirmative predesignation is to be connected with the
predicate, as when Aristotle himself styles the soul a certain {some)
a It will be observed, that Ammo- trine; and this impossibility itself ought
nius does not attempt an equivalent for to have opened his eyes upon the insuf-
this proposition. In fact it is impos- ficiency of the view he maintained,
sible on the common or Aristotelic doc-
APPENDIX. 305
entelecliT, JfTekexeLoiv Tiva\ and Plato, rhetoric, a certain (soine)
experience. [ifJureLpiav tlvo) ; it is to be observed that the some
is there added for the sake of showing, that the predicate is not
convertible with the subject, but is its genus, and requires the
adding on of certain differences in order to render it the subject's
definition.
" But, add they, is not the reasoning of Aristotle refuted by
fact itself, seeing that we say, All man is capable of all science :
thus truly connecting the universal predesignation with the uni-
versal predicate ? The answer is this : — that, in truth it is not the
predicate to which we here annex the all For what is predi-
cated, is what is said of the subject. But what is here said of
man is. not that he is science, but that he is capable of science.
If, therefore, the all were conjoined with the capable and the
proposition then to remain true, as when we say — all man is all
capable of science; in that case, the reasoning of Aristotle would
be refuted. But this proposition is necessarily false. It, in fact,
asserts nothing less, than that of men, each individual is all
the kind ; — that Socrates is not Socrates only, but also Plato,
Alcibiades, and, in short, every other man. For. if all man is all
capable of science, Socrates beiug one of the all, is, therefore,
himself all capable of science ; so that Socrates will be Plato,
Alcibiades, &c., since they also are capable of science. For if
Socrates be not, at once, Plato, Alcibiades, &c., neither wiU he be
all capable of science
■' Xow, that we ought not to prefix the universal affirmative pre-
designation to the predicate, (whether the predicate be more gene-
ral than the subject, as All man is all animal, or, whether they be
co-adequate, as All man is all risible,) — this is manifest from
what has been said. Even when the terms are coadequate or re-
ciprocating, the proposition runs into the absurd. For, declaring
that all man is all risible, it virtually declares, that each indi-
vidual man is identical with all men ; that Socrates, in that he is
a man, is all 7'isihle, consequently, all man
" But why is it, that the predicate is intolerant of the predesig-
nation all. though this be akin to the counter-predesignation no
or none ? Is it because the affii'mative predicate, if predicated
universally, tends always to contain under it tlie subject, and this
not only when itself coadequate with the subject, but when trans-
VOL. II, U
30G APPENDIX.
cending the subject in extension ; while, moreover, through a parti-
cipation in its proper nature, it is suited to bind up and reduce to
unity the multitude of individuals of which the subject is the
complement ? For, as Aristotle previously obseiTcd — ' The all
does not indicate the universal, but that [the universal predicate
inheres in, or is attributed to, the subject] universally.' If, there-
fore, the affirmative predicate thus tend to collect into one what
are by nature distracted, in virtue of having been itself previously
recognised as simple ; in this case, the all, [superadded to this
universal predicate, in fact], enounces not a unity, but a multitude
of several things, — things which it is manifestly unable to compHcate
into recij)rocity. But, on the other hand, since what is negatively
predicated of, is absolutely separated from, the subject ; we are,
consequently, enabled to deny of the subject all under the predicate,
as in saying. All vian is no stone. We may indeed condense
this proposition, and say more simply. All man is not stone ; or
more simply still. No man is stone ; thus dispensing with the
affirmative j)redesignation in a negative proposition."
IV. — BOETHIUS.
Boethius,/w Lihrum de Interpretatione, editio secunda,et in tex-
tum laudatum. Opera, jj. 848.
" What he says is to this purport : — Every simple proposition
consists of two terms. To these there is frequently added a de-
termination either of universality or of particularity ; and to
which of the two parts these determinations are to be added, he
expounds. It appears to Aristotle that the determination ought
not to be conjoined to the predicate term ; for in this proposition,
Man is animal — {Homo est animal) it is inquired whether the
determination ought to be coupled with the determination, so that
it shall be — (Oninis homo animal est) — All (or every) man is ani-
mal ; or with the predicate, so that it shall be, — {Homo omne ani-
mal est) — Man is all (or every) animal ; or with both tlie one and
tlie other, so that it shall be. All (or every) man is all (or every)
animal, {Omnis homo omne animal est). But neither of these
latter alternatives is competent. For the determination is never
joined to the predicate, but exclusively to the subject ; seeing
that all predication is either greater than the sulyect, or equal.
APPENDIX. 307
Thus ill this proposition — All (or every) man is animal, (omnis
homo oMimal est), animal [the predicate] is greater than man
[the subject] ; and, again, in the proposition — Man is risible,
(homo risihilis est), risible [the predicate] is equated to man [the
subject] ; but that the predicate should be less and narrower than
the subject is impossible. Therefore, in those predicates whichi are
greater than the subject, as, for example, where the predication is
animal, the proposition is manifestly false, if the determination of
universality be added to the predicate term. For if we say, Man
is animal, (homo est animal), we contract animal, which is greater
than man^ by this determination to [an identity of extension with]
man, the subject, although the predicate, animal, may be applied
not only to man, but to many other objects. Moreover, in those
[subjects and predicates] which are equal, the same occurs; for if I
say. All (or every) man is all (or every) risible, (omnis homo omne
risibile est), — in the first place, in reference to the nature of man
itself, it is superfluous to adject the determination ; and, again,
if this be added to all several men, the proposition becomes false,
for when I say. All (or every) man is all (or every) risible, by this
I seem to signify that the several men are [each of them] all or
every risible, which is absurd. The determination is, therefore, to
be placed not to the predicate but to the subject. But the words
of Aristotle are thus reduced to the following import : — In those
predicates which are universal, to add to them aught universal,
so that tJie universal predicate may be predicated universally,
is not true. For this is what he says — " In the case of a univer-
sal predicate," (that is, in a proposition which has an universal pre-
dicate), " to predicate the universal, itself universally, is not true.'"
For in an universal predicate, that is, which is universal and is
itself predicated, in this case universally to predicate the predi-
cate which is universal, that is, to adject to it a determination of
universality, is not true : for it cannot be that any affirmation
should be true in which a universal determination is predicated of
a predicate universally distributed ; and he illustrates the concep-
tion of the matter by the example, " All or every man is cdl (or
every) animal, (omnis homo omne animal est), of the incompe-
tency of which we have already spoken."
Boethius, In Librum de I nterpr elation e, editio prima. Opera,
808 APrENDIX.
p. 236. (Text so wretchedly printed that the sense must be con-
stituted by the reader. )
[Aristotle, c. vii. § 4], " ' In what is predicated as an universal,
to predicate the universal universally is not true/
" In this sentence he instructs us what is the place to which the
determination of universality should be rightly added. For he
teaches that the universality, which we call the universal determi-
nation, is to be connected with the subject term, never with the
predicate. For were we to say — All (or every) man is animal,
{omnis homo animal est), we should say rightly, annexing the
all (or every) to the subject, that is, to the term Tnan. But if we
thus speak — All or every man is all or every animal, {omnis
homo omne animal est), we should s-peak falsely. He, therefore,
does not say this [in the words] — ' in what is predicated as an
universal,' as animal of man ; for animal is universal, being pre-
dicated of all or every man. [But he says] — To predicate this
universal itself, anim^al, to wit, universally, so that we enounce
— All (or every) animal is man, {omne animal esse hominerro), is
not true ; for he allows this to be rightly done neither iii these nor
in any other affirmation.* He adds, therefore ; — ' For no affirma-
tion will be true in which a universal predicate shall be univer-
sally predicated, as All or every man is all or every animal,
{omnis homo est omne animal).'
"Why this happens, I will exi^lain in a few words. The
predicate is always greater than the subject, or equal to it.
Greater, as when I say Han is animal, {homo animal est) ; here
animal is predicated, man is subjected, for animal is predicated of
more objects than man. Again, it is equal when we thus speak —
Man is risible, {homo risibilis est) ; here man is the subject,
risible the predicate. But man and risible are equal ; for it is
proper to man to be a risible animal. But that the predicate
a The Coimbra Jesuits (Sebastianus by their brother Jesuit, P. Vallius of
Contus, 1606), erroneously make Boe- Rome, in his mighty Logic [ad locum).
thiua and Averroes oppose Aristotle, With Boethius he joins Levigersonides ;
" thinking that the sign of universality — he means the Rabbi Levi Ben Gerson,
may be annexed to the predicate of a of Catalonia, who died at Perpignan in
universal proposition, when it is coexten- 1370, who wrote on Theology, Philoso-
sive with the subject," (arf locum ii., p. phy, Mathematics, and Logic. SeeJocher
158). This, a mistake, has been copied v. Levi, from Bartolocci and Wolf.
APPENDIX. 309
should be found less than the subject, is impossible. Is the predi-
cate the greater ? Then, to adject the universal to the predicate, is
false, as in the example he himself has given — All (or every) man
is all (or every) animal, {omnis homo omne animal est). Is it
equal ? Then, the adjection is superfluous, as if one should say. All
every man is all or every risible, [omnis homo omne risibile
est). Wherefore, to predicate a universal predicate universally is
incompetent."
V. — AVEEKOES.
Averroes, Perihermenias, L. I., c. v.
" Propositions are not divided from the conjunction of the pre-
designation (clausurse) with the predicate ; because the predesig-
nation, when added to the predicate, constitutes a false or a super-
fluous proposition : — False, as All or every man is all (or every)
animal, (omnis homo est omne animal) ; suijerfluous, as All (or
every) man is some or a certain animal, (omnis homo est quod-
dam animal)." Vide Conimbricenses, In Arist. Dial., ii. lo8.
VI. — Albeetus Magnus.
Albertus Magnus, Periherminias, L. I., Tractatns, v. c. 1, (Op.
ed. Lugd. 1651, t. I, p. 2G1).
[" Ly ' oTunis' non est universale, sed signum universalitatis.
Quare ly ' omnis' et hujusmodi signa distributiva non sunt uni-
versalia, secundum Avicennam" ]. Hoc enim signum distri-
butivum, quod est omnis, non est universale, proprie loquendo :
sed est signum per quod stat pro particularibus universaliter uni-
versale, cui tale signum est adjunctum. Causa autem, quare non
sit universale, est : — quia, quamvis secundimi grammaticum sit
nomen appellativura, hoc est, multis secundum naturae sure apti-
tudinem conveniens ; tamen est, secundum formam, infinitum,
nuUam enim naturam unam dicit. Propter quod omnis naturae
communis est distributivum. Universale autem est, quod est in
multis et de multis, su?e naturse, suppositis. Ideo omnis, et
mdlus, et hujusmodi signa universalia esse non possunt ; sed
sunt signa designantia utrum universale sit acceptum universaliter
i
310 appp:ndix.
vel particiilariter, secundum sua supposita. Et ha?c sunt verba
Avicennrei.
[ " Quare signum universale non sit ponendum a parte
prredicati.] In subjecto universali signum distributivura ordi-
nandum : quia per divisionem subjecti, pmedicatum partibus
attribuitur subjecti, ut divisim participent id per pradica-
tionem, et non in praedicato ponendum : quia quum praedicatum
formaliter sit acceptum, non proprie dividitur, nisi alterius, hoc est,
subjecti divisione : sed insequaliter redditur subjecto et partibus
ejus. Unde id quod est universale, preedicari potest, ut Omnis
homo est animal ; sed universale universaliter acceptum non po-
test prtedicari ; nulla enim vera affirmatio esse potest, in qua de
universaK aliquo prsedicato predicetur sive prsedicatio fiat ; quo-
niam universaliter sic patet, quod falsum est, Onmis homo est
omne animal, et si ponatur, quod Nullum animal sit nisi homo.
Cum enim homo subjiciatur gratia partium suarum, et pregdi-
cata formaliter accipiantur, oportet quod Quilihet homo esset
omnc animal, quod falsum est."
VII— Levi Ben Geeson.
Levi Ben Gerson (or Levi Gersonides), a Jewish philosopher,
Avho died in 1370 at Per2)ignan, wrote commentaries on Averroes'
Commentary upon the logical books of Aristotle. The following is
what he says on Averroes' doctrine touching the quantification of
the predicate, as it is found (f. 3D) of the Venice edition, in folio,
of lo.52,a of the works of Aristotle and Averroes: — "Although
it be not necessary that when the quantitative note is attached to
the predicate, this should be false or superfluous, seeing that it
may be neither, as when we say. All man is all rational ; and the
same holds good in all other reciprocating propositions ; — never-
theless, as in certain matters it may so happen, Aristotle has de-
clared that the quantitative note is not to be joined to the predi-
cate in any language. But it may be here objected, that if this
be the case, the quantitative note should not be annexed even ta
the subject, since there too it may be eitlier false or superfluous.
Superfluous, — as when we say. Some animal is rational. For the
very same follows here, as if we simply say, Animal is rational ;
a Not iu the 8vo edition of these works. Venice, 1560.
APPENDIX. 311
the some, therefore, is superfluous. False, — as when we say, All
animal is rational. The reason, therefore, assigned by Aristotle
why the quantitative note should not be annexed to the predicate,
is futile, seeing that for the same reason it should not be connected
with the subject. To this we may answer: That the cause why
the quantitative note is not usually conjoined with the predicate,
is, that there would thus be two quassita at once, — to wit, whether
the predicate were affirmed of the subject, and, moreover, whether
it were denied of everything beside. For when we say. All man
is all rational, we judge that all man is rational, and judge, like-
wise, that rational is denied of all hut man. But these are in
reality two different qua3sita ; and therefore it has become usual
to state them, not in one, but in two several propositions. And
this is self-evident ; seeing that a qupesitum, in itself, asks only —
Does, or does not, this inhere in that ? and not — Does this inhere
in that, and, at the same time, inhere in nothing else ? "
VIII. — The Masters op Louvain.
Facultatis Artiuin in Academia Lovaniensi Commentaria in
Ai^istotelis Lihros de Dialectica,{loS5),Tr. iii. c. l,p. 162, ed.l547.
Speaking of the text in the De Inter pretatione, the Masters, inter
alia, allege : " But if it be even elegantly said by a poet — ' Nemo
est omnis homo,' — ' Non omnes omnibus artes' — [proverb, ' Unus
homo nuUus homo '], why may we not contradict this aptly,
howbeit falsely, — ' Aliquis est omnis homo' ? Why, (tliey say), do
you determine the predicate by the note of universality, seeing
that the quantity of the proposition is not to be sought from the
predicate, but from the subject ? We answer, because we wish
to express a certain meaning in words, which by no others can be
done. But if the mark of universality could only be employed in
changing the quantity of propositions, it would not be lawful to
annex it to the part of the predicate. We have, therefore, thought
these few cautions requisite to evince that what is condemned by
these critics for its folly, is not incontinently sophistical or foolish
babbling. But as to the universal rule which Aristotle enounces,
— 'No affirmation will be true,' &c. — it is sufficient if it hold good
in the majority of cases; whether the predicate exceed the subject,
as. All man is all animal, — be its equal, as, All man is all 7'isible,
312
APPENDIX.
or its inferior, as, [So7ne] animal is all man. In a few cases,
however, the exception is valid ; as, — This sun is every sun, One
phoenix is all plicenix, and some others. Nor are these futile
subtleties, since reason herself approves.'"'
IX. — TiTIUS AND RiDIGEK.
The only notice of these speculations of Titius,a which I have
met with in any subsequent philosopher, (and I speak from an
insijection of several hundred logical systems, principally by Ger-
mans), is his friend Eidiger's ; who in his elaborate work De Sensu
Veri et Falsi, first published some eight years subsequently, (in
1709, but I have only the second edition of 1722), attempts a
formal refutation of the heresy of a quantified predicate. It was
a [Titius, Jrs Cogitandi, c. vi., has the
following relative to the quantification
of the predicate]: — § 36, " Licet autem
Proi^ositionum quantitas ex Subjecto
a3stimetur, attamen Prsedicatum nou
penitus negligendum videbatur, ceu vul-
go in hoc tractatione fieri solet, nam et
hujus quantitatem observasse utile est,
et crediderim et disquisitionis hujus
neglectu varios eiTores tam in doctrina
Conversionis, quam Syllogistica esse ex-
ortos, quos suis locis videbimus. § 37,
Breviter itaque observandum,in proposi-
tionibus affirmativis, licet universalibus,
prasdicatum plerumque esse particulare,
tribuique subjecto secundum totam qui-
dem suam compreliens'wnem, non vero
ex ten si one m. § 39, E coutrario in propo-
aitionibus negativis, licet particularibus,
plerumque prasdicatum est uiiircrsale,
ac tam secundum comiirehensionem
quam extensionem suam totam, a sub-
jecto removetur. § 41, Interim non pu-
tarem affirmationem vel ncgationem
ipsam diversam illam prajdicati quan-
titatem necessario postulare, sed credi-
derim potius, id omne a diverse rerum
et idearum habitu oriri, affirmation!
vero et negation! prredicati quantita-
tem esse velut indiiTerentem. § 42,
Nam plerumque prajdicata subjectis sunt
latiora ; quodsi igitur ilia cum his com-
ponas, non poterit nou prasdicatum jiar-
ticulare iude emergere, dum unice ad
subjectum restringi nequit, sed ad alia
quoque extendi aptum manet. § 43,
Ast si praidicatum a subjecto I'emoveas,
universale illud erit, cum quicquid in
ejus vel comprehensione vel extensione
est ab hoc sejungatur, nee imminuit
uuiversalitatem, quod idem ab aliis sub-
jectis quoque removeatur, nam si prse-
dicatum aliis etiam conveniat, tum qui-
dem uni subjecto non potest dici uni-
versaliter tributum, verum si de multis
negetur, potest nihilominus de certo
aliquo subjecto uuiversaliter quoque ne-
gari. § 44, Quodsi habitus attributi
permittat, poterit aliquando propositio
affirmativa pra3dicatum universale, et
negativa particulare habere ; nihil enim
obstat, quo minus aliquando totum al-
ter! jungere, vel partem ab eodem re-
movere queas. § 45, Ha2C itaque pro-
posititio : — Omnis homo est risibilis,
habot pra?dicatum univei'sale, si risibili-
tatem 2)ro homiuis proprio habeas; sicut
ha3, — Nullus Turca est homo, (Scil. Chris-
tkmus),ye\ Quidam mcdicus non esthomo
quidam, pnedicatum particulare conti-
nent, dum pars solum comprehensiouis
et extensionis removetur." For the
application, by Titius, of the principle of
a quantified predicate to the doctrine of
Conversion, see above pp. 274, 275; and
to the theory of Syllogism, see below,
p. 375, and Appendix, X. — Ed.]
APPENDIX. 813
only, however, after " the most manifest demonstrations of the
falsehood of this novel prejudice had been once and again privately
communicated to his very learned friend, " (Titius ?), that Kidiger
became at length tired, as he expresses it, " of washing a brick,"
and laid the polemic before the f)ublic. It was not certainly the
cogency of this refutation which ought to have thrown the counter
opinion into oblivion ; but this refutation, such as it is, though
with nothing new, is deserving of attention, as presenting the most
elaborate discussion of the question to be met with, after Am-
monius, and in modern times. But the whole argument supposes
certain foundations ; and it will be sufficient to show that these
are false, to dispose of the whole edifice erected upon them. I
ought to mention, that it was Kidiger's criticism which first directed
my attention to the original of Titius.
" Origo autera hujus erroris neglectus notissimse acquivoca-
tionis signorum omnis et quidam esse videtur, qua h?ec signa,
vel collective sumi possunt, vel distributive. Priori modo, quan-
titas in prsedicato concepta sensum quidem infert non penitus
absurdum, cpeterum propositionem constituit identicmm et frus-
traneam." Ridiger then goes on to a more detailed statement
of what he supposes to be the grounds on which the erroneous
opinion proceeds."
First Case. — " Verbi gratia, Quoddam animal est omnis homo ;
hoc est. Species qucedam animalis, homo nemioe, omne id, quod
homo est : quod alium sensum, habere nullum potest, quam, quod
omnis homo sit homo : sic autem collective sumitur et signum
subjecti et signum prsedicati." This objection is absurd, for it is
suicidal ; applying equally to the proposition which the objector
holds for good, and to that which he assails as bad. All man is
(some) animal. Here, is not animal or some animal, just a
certain species of animal, and is not this species, man, to wit, all
that is man, and nothing else ? There is, consequently, the same
tautology in the one case as in the other ; and if we are blamed
for only virtually saying, by the former. All man is man, does
the objector say a whit more than this, by the latter ? Ridiger
goes on : " Quodsi vel alteram signum, vel utrumque, distributive
sumatur, semper absurdus erit propositionis sensus."
« Second Edition, pp. 232, 302.
314 APPENDIX.
Second Case. — " Verbi gratia, sumatiir uti'umque signum distri-
butive, sensus erit, Quoddam individuum animalis, (v. g. Fetrus,)
est omne individuum hominis, (v, g. Davus, Oedipus)." This is a
still higher flight of absiuxlity ; for, to refute tlie proposition, it is
lirst falsely translated into nonsense. Its true meaning, both
quantified terms being taken distributively, is : — All several men
are some several animals, or, Every several man is some several
animal.
In these two cases, therefore, all is correct, and the objection
from the identity or absurdity of a quantified predicate, null.
Third Case. — " Sumatur signum subjecti distributive, signum
prffidicati collective, sensus erit : Quoddam individuum animalis
est U7iiversa species hon^inisy
Fourth Case. — " Sumatur, denique, signum subjecti collective,
signum j)r9edicati distributive, sensus erit : Quwdam species ani-
malis, ut universale et ptrwdicabile, est omne individuum hominis."
In regard to these last two cases, it is sufficient to refer to what
lias been already said in answer to Ammonius (p. 296) ; or simj^ly
to recall the postulate, that in the same logical unity (proposition
or syllogism) the terms should be supposed in the same sense. If
this postulate be obeyed, these two cases are inept, and, conse-
quently, the objections superfluous.
Ridiger then proceeds to treat us with four long " demonstra-
tions a p7-iori,^' and to one elaborate " demonstration a posteriori ;"
but as these are all founded on the blunders now exposed, it would
be idle to refute them in detail.
Ridiger, it m.ay well surprise us, howbeit the professed cham-
pion of " the old and correct doctrine," is virtually, perhaps uncon-
sciously, a confessor of the truth of " the new and false prejudice ; "
for I find him propounding four several syllogistic forms, three of
which are only valid through the universal quantification of the
predicate in affirmatives, and two, (including the other one), 2:)roceed
on a correct, though partial, view, opposed to that of the logicians,
touching the conclusion of the Second Figure, (L. II. c. vi.) I
shall insert the quantities, operative but not expressed.
In the First Figure — " At, aut ego nihil video, aut lorge natu-
rali or est hie processus : — Quoddam fluidum est [quoddam] leve;
quoddam corpus est \ovine] fluidum ; ergo quoddam corpus est
quoddam leve; quam si dicas, &c., (§ 34<). — Here the middle
APPENDIX. 315
term is, and must be, affirmatively distributed as predicate.
In the Second Figure. — " Verbi gratia: — Quoddani ens est
[omne^ ani7nal : omnis homo est [quoddani\ animal; ergo, ornnis
homo est [quoddam] ens. Hsec conclusio verissima, &c." (§ 89.)
In like manner the middle is here universally quantified in an
affirmative, f'luiiiiin M,^.^^iB: r.
The following, Eidiger (p. 330) gives, as "two new moods,
which cannot be dispensed with." — "Quoddani animal est [oninis]
homo ; mdliim hrutum est \tdlus^ homo ; ergo, quoddam animal
7ion est [ullum] hrutum.'' Item : — Quoddam animal non est
\idlus] homo ; omnis civis est [quidam] homo ; ergo, quoddam
animal non est [ullus] civis." — In the first of these, the middle,
as predicate, is affirmatively distributed ; and in both syllogisms,
one conclusion, denied by the logicians, is asserted by Ridiger,
although the other, which involves a predicate, particular and
negative, is recognised by neither.
X. — Godfrey Ploucquet.
Godfrey Ploucquet, a philosopher of some account, Professor
of Logic and Metaphysic in the University of Tubingen, by various
writings, from the year 1759, endeavoured to advance the science
of reasoning ; and his failure was perhaps owing more to the
inadequacy and limitation of his doctrine, than to its positive
error. To say nothing about his attempt to reduce Logic to a
species of computation, in which his one-sided views came into
confliction with the one-sided views of Lambert, he undoubtedly
commenced auspiciously, on the principle of a quantified predicate.
This, like a few preceding logicians, he certainly saw afforded a
mean of simplifying the conversion of propositions ;« but he did
not see that it could accomplish much more, if properly applied,
o An extract from his Fundamcnta quantification of the predicate, will be
PhllosopJiia' Speculative, 1759, contain- found in Mr Bayues' Essaij, p. 128.
ing Ploucquet'i3 doctrine touching the
31 G APPENDIX.
in the theory of syllogism. On the contrary, in syllogistic, he pro-
fessedly returns, on mature consideration, to the ordinary jjoint
of view, and thinks himself successful in recalling the common
doctrine of inference to a single canon. That canon is this : —
" The terms in the conclusion are to be taken absolutely in the
same extension which they hold in the antecedent." — " In conclusi-
one sint termini jjlane iidem, qui in prtemissis, intuitu quantitatis."
{Methodus tarn demonstrandi directe omnes syllogismorum
species, quam vitia formce detegendi, ojye unius regidce; — Me-
thodus calcvlandi in Logicis ; i^assiin. Both in 1763). This
rule, as applied to his logical calculus, he thus enounces: "Arrange
the terms in syllogistic order ; strike out the middle ; and the
extremes then afford the conclusion." — " Deleatur in praemissis
medius ; id quod restat indicat conclusionem." {Methodus calcu-
landi, imssiin ; Elementa Philosopldce Contemplative^, Logica,
§ 122, 1778.) This rule is simple enough, but, unfortimately, it is
both inadequate and false Inadequate (and this was ahvays
sufficiently apparent) ; for it does not enable us to ascertain, (and
these the principal questions), how many terms, — of what identity
• — of what quantity — and of what quality, can be legitimately
jilaced in the antecedent. But it is not true, (though this was
never signalised) ; for its peculiar principle is falsified by eight of
the thirty-six moods, to wit, in affirmatives, by ix., x., xi., xii., and
in negatives, by ix, b, x. a, xi. b, xii. a.a In all these, the quan-
tity of an extreme in the conclusion is less than its quantity in the
antecedent. We can hardly, therefore, wonder that Ploucquet's
logical sj)eculations have been neglected or contemned ; although
their author be an independent and learned thinker, and his works
all well worthy of perusal. But, though dismissed by Hegel and
other German logicians, not for its falsity, with sujireme contempt,
Ploucquet's canon has, however, found its admirers in this country,
where I have lately seen it promulgated as original.
XI. — Uleich.
Institutiones Logicce et Metaphysical, § 171, 1785. — "Non
tantum subjecto ^ed et p7'cedicato, ad subjectum relato, sua constat
quantitas, suumque igitur signum quantitatis prsefigere licet. Sed
hgec prsedicati quantitas ex veterum prseceptis ssepe justo minor
o See Table of Moods below. Appendix, XI. — Ed.
APPENDIX. 317
invenitur. In loco de conversione distinctius de eo exponetur."
In that place, however, nothing of the kind appears.a
IV.
CANONS OF SYLLOGISM; GENEEAL HISTORICAL
NOTICES AND CRITICISM.
A. HISTOEICAL NOTICES.
(a) QUOTATIONS FROM VAEIOUS LOGICIANS.
(Collectecl and Translated Autumn 1844. See above, Vol. I. p. 303. — Ed.)
I — David Derodon.
David Derodon (who died at Geneva in 1664-, and had been
previously Professor of Philosophy at Die, Orange and Nismes),
was a logician of no little f;xme among the French Huguenots ; the
study of his works was, (if I recollect aright), even formally recom-
mended to the brethren of their communion, by one of the Galli-
can Synods. " Either the Devil or Doctor Derodon," was long
a [That the Extension of Predicate is pp. 158, 283. Scotus, In An. Prior. L. i.
always reduced to Extension of Subject, qu. 4,f. 240 ; qu. 13, ff. 254'', 255* ; qu.
i.e., is equivalent to it, see Purchot, 14, f. 256''; qu. 23,f. 273*.
Jnstit. Phil., Logica, i. pp. 123, 125. For instances of Aristotle virtually
Ttslcy, El&niens d'Ideoloffie, t. iii. Disc, using distributed predicate, see .4 n.Pos^
Prel., pp. 99, 100. Cronsaz, Logique, t. i.6,% I. Cf. Zabarella, cul he. Opera
iii. p. 190. Derodon, Zo^/ca Restituta, Logica, p. 7^5. The sa.me, In An. Post.
P. ii., c. v., art. 4, p. 224. Boethius, O^JO'ct, I. 2. Opera, p. 827, and De Quarto,
p. 348, (see above, p. 306). Sergeant, Figura Sijllog. Op., -p. 123. The adding
Method to Science, b. ii., less. i. p. 127. mark of universality to predicate is,
Beneke, Lehrhuch der Logik, § 156, p. Aristotle says, " useless and impossible"
100. Stattler, Logica, § 196. (An Prior., i. c. 27, § 9); yet see ii. c.
That the Predicate has quantity ; and 22, §§7, 8 ; c. 23, §§ 4, 5. On this
potential designation of it as well as question, see Bolzano, Logik, % 131, p.
the Subject, see Hoffbauer, Analytih 27, (and above, pp. 295, 301, 302.)
der Urtheile und Schliisse, § 31 e< seq. That the predesignation of the predi-
Lambert, Deutsclier Gelehrter Prie/tcech- cate by all collectively, in fact, reduces
sel, Brief vi. vol. i. p. 395. Platner, the univei'sal to a singular proposition,
Philosophischc Aphorismen, i. § 546. see Purchot, Instit. Phil., i. p. 124. Cf.
Corvinus, Instit. Phil. Pat., § 413. Logica Contractu Trajectina, P. ii. c. 5.
Conimbricenses, In Ai'ist. Dial., t. ii. (1707.)]
818 APPENDIX.
a proverbial expression in France for tlie authorship of an acute
argument ; and the " Sepulchre of the Mass" has been translated
into the vernacular of every Calvinist country. Derodon has left
two systems of Logic ; a larger, {Logica Restituta, 1659), and a
smaller {Logica Contracta, 1664), both published in 4to.a I shall
quote only from the former.
It is impossible to deny Derodon's subtlety, but his blunders
unfortunately outweigh his originality. Leaving Conversion as he
found it, after reiDcating, with approbation, the old rules, — that the
predicate is not to be overtly quantified universally, (p. 573), but
to be taken, in affirmative propositions particularly, as in negative
propositions universally, (p. 623) ; we are surprised to find him
controverting, in detail, the special rules of syllogism. This polemic,
as might be exj^ected, is signally unsuccessful ; for it is frequently
at variance with all principle, and uniforndy in contradiction of his
own. It is, indeed, only interesting as a manifestation, that the old
logical doctrine was obscurely felt by so original a thinker to be
erroneous ; for the corrections attempted by Derodon are, them-
selves, especially on the ground which he adoj^ts, only so many
errors. He unhappily starts with a blunder ; for he gives, as rectus,
an examjile of syllogism, in which the middle term is, even of ne-
cessity, undistributed ; and he goes on (pp. 627, 628, 636, 637, 638,
639, 619) either to stumble in the same fashion, or to adduce rea-
sonings, which can only be vindicated as inferential, by supplying
a universal quantity to the predicate in affirmative propositions,
or by reducing it to particularity in negatives ; both in the teeth
of Derodon's own laws. I have, however, recorded, in my Table of
Syllogisms, some of his examples, both the two forms which he has
named, and four others which he only enounces ; according, by
liberal construction, what was requisite to give them sense, and
which, without doubt, the author would himself have recognised.
II. — Eapin.
Rapin, Reflexions sur la Logique, § 4, 1684.
" Before Aristotle there had appeared nothing on logic systematic
« Derodon seems wholly unknown to a considerable number in the .^amebind-
the German logicians, and, I need hardly ing must have been imported at once,
add, to those of other countries. In probably in consequence of the synodical
Scotland his works are not of the rarest ; recommendation.
APPENDIX. 819
and established. His genius, so full of reason and intelligence,
penetrated to the recesses of the mind of man, and laid open all
its secret workings in the accurate analysis wMch he made of its
operations. The depths of human thought had not as yet been
fathomed. Aristotle was the first who discovered the new way
of attaining to science, by the evidence of demonstration, and of
proceeding geometrically to demonstration, by the infallibility of
the syllogism, the most accomplished work and mightiest effort of
the human mind," &c.
Rapin errs in making Aristotle lay the rule of proportion along
with the Dictum de Omni as a princijile of syllogism.
Ill— Leibnitz.
Leibnitz, De la confoi'mite de la Foi avec la Raison, § 22.
Op. t. i., p. 81. " Hence the facility of some WTiters is too great,
in conceding that the doctrine of the Holy Trinity is repugnant
with that great principle which enounces — What ai'e the same
with the same third, are the same with each other ; that is, if A
be the same with B, and C be the same with B, it is necessary that
A and C should also be the same with one another. For this
principle flows immediately from the principle of Contradiction,
and is the ground and basis of all Logic ; if that fail, there is no
longer any way of reasoning with certainty."
IV.— Reusch.
Reusch, Sy sterna Logicum, 1734.
§ 506. "That dictum of the Aristotelians de Omni et Kidlo,
(503), evinces, indeed, a legitimate consequence, but it only regu-
lates one species of syllogisms, at least immediately. By this reason,
therefore, logicians have been induced to prove the consequence of
the other sj)ecies by means of the first, to which they are reduced.
But, that we may be able to supersede this labour, I have en-
deavoured to give a broader basis to the Dictum de Omni et Nullo,
or by whatever name that rule is called, to which, in the construc-
tion of syllogisms, the order of thought is conformed.
§ 507. " For the whole business of ordinary reasoning is accom-
plished by the substitution of ideas in place of the subject or predi-
320 APPENDIX.
cate of the fundamental proposition. This some call the equation
of thoughts. Now, the fundamental proposition may be either
affirmative or negative, and in each the ideas of the terms may be
considered either agreeing or diverse, and according to this various
relation there obtains a various substitution, which we shall clearly
illustrate before engaging with our doctrine of the Dictum de
Omni et Nullo." [Having done this at great length, he proceeds].
§ "510. From what has been now fully declared, the following
Dictum de Omni et Nullo may be formed, which the definition
itself of reasoning and syllogism (§ 502) supports, and to which
all syllogisms in every figure and mood may be accommodated.
"If two ideas (two terms) have, through a judgment, (proposi-
tion), received a relation to each other, either affirmative or nega-
tive, in that case it is allowable, in place of either of these, (that
is, the subject or predicate of that judgment or proposition), to sub-
stitute another idea, (term), according to the rules given of Equi-
poUence or Reciprocation (§ 508, s. 9), of Subordination, of Co-
ordination," (see Waldin, below, p. 824!).
IV.— Ceusius.
Crusius, Weg zur Gewissheit. Ed. i. 1747; Ed. ii. 1762.
§ 256. " The supreme law of all syllogism is. What we cannot
otherwise think than as true, is true, and what we absolutely can-
not think at all, or cannot think but as false, isfalse."^
§ 259. Of necessary judgments, of judgments which we cannot
but think, " which are not identical, and which constitute, in the
last result, the positive or the kernel in our knowledge ; to which
we apply the principle of Contradiction, and thereby enrich the
a Kant, {iiber die. Evidenz in mefa- if it be agreed that no other principle
physischen Wissenschaftcn, 1763, Verm, of truth is possible than inasmuch as
Schrift. ii. 43), has hereon the following we are incapable of holding a thing not
observation : — "In regard to the su- for true, in this case it is acknowledged
preme rule of all certainty which this that no other principle of truth is corn-
celebrated man thought of placing as petent, and that knowledge is indemon-
the principle of all knowledge, and, strable. It is indeed true that there are
consequently, also of the metaphysical, many indemonstrable knowledges, but
What I cannot otherwise think than as the feeling of conviction in regard to
true is true, &c. ; it is manifest that this them is a confession, but not a ground
proposition can never be a principle of of proof, that they are true." — See also
truth for any knowledge whatever. For Reid, Inlellcctual Powers, Esmy iv. ch. 4.
APPENDIX. 321
understanding with a knowledge of real judgments," — such judg-
ments are principally the following : Every power or force is in-
herent in a subject ; All that ai^ises, (begins to be), arises in virtue
of a suffi^cient cause; All whose non-existence cannot be thought,
has its cause, and has at some time arisen, (begun to be) ; Evei^
substance exists somewhere ; All that exists, exists at some time;
Two7naterial things cannot exist at the same time,and in jprecisely
the same j^lace. There are also many other propositions, which
treat of the determinate qualification of things as present ; for ex-
ample — The same point of a body cannot be at once red and green ;
A man cannot be in two places at once, and so forth.
" § 261. All the judgments previously alleged, (§ 259), may be
comprehended under these two general propositions, — What can-
not in thought be separated from each other, cannot be separated
from each other in reality ; and, What cannot in thought be con-
nected into a notion, cannot in reality be connected; to vAi,
although no contradiction shows itself between the notions, but we
are only conscious of a j)hysical necessity to think the thing so and
so, clearly and after a comparison of all the circumstances with
each other. For we now speak of jiropositions which are not
identical with the Principle of Contradiction, but of such as prima-
rily afford the matters on which it may be applied. Hence we see
that the supreme principle of our knowledge given above, (§ 256),
has two determinations ; inasmuch as the impossibility to think a
something arises, either because a contradiction would ensue, or
because we are positively so compelled by the physical constitution
of our thinking faculties.
"§ 262. The highest principle of all syllogism thus resolves itself
into the three caj^ital propositions ;
1. Nothing can at once be and not be in the same j^oint of view.
2. Things which cannot be thought without each other, without
each other cannot exist.
3. What cannot be thought as with and beside each other, can-
not exist with and beside each other, on the supposition even that
between the notions there is no contradiction.
"The second of these capital propositions I call the Principle
of Inseparables, {principiuni inseparabilium) ; and the third
the Principle of Inconjoinables, {principium inconjungibilium).
They may be also termed the three Pj^inciples of Reason.
VOL. II. X
II
322 APPENDIX.
Cli. VIII. Of the different sjiecies of syllogisms, he says, (§ 272),
"among the higher principles of syllogisms it is needful only
to enumerate the Principle of Contradiction, and the Principle
of Su^cient Reason, w\\\c\\ is subsumed from the principle of In-
separables, (§ 262). We shall state the laws of syllogism in this
order, — Consider those which flow, 1°, Prom the Principle of
Contradiction ; 2°, Erom the Principle of Sufficient Reason ; and,
3°, From both together."
V. — Francis Hutcheson.
[Francisci Hutcheson.] Logicm Compendium. Glasguce, in
wdibus academicis, excudebant Rohertus et Andreas Foidis, Aca-
demice Typograplii. 1764.
Part III., Ch. ii.. p. 58.
" The whole force of syllogism may be explicated from the fol-
lowing axioms.
" First Axiom. — Things which agree in the same third, agree
among themselves.
" Second Axiom. — Things whereof the one agrees, the other
does not agr-ee, in one and the same thij-d, these things do not
agree among themselves.
" Third Axiom. — Things which agree in no tliird, do not agree
among themselves.
Fourth Axiom. — Things which disagree in no third, do not
disagree among themselves!'
" Hence are deduced the general rules of syllogisms.
"Of these the three first regard the Quality [not alone] of Pro-
positions.
" Rule 1. — If one of the premises he negative, the conclusion
will he negative (by Ax. 2).
"Rule 2. If hoth premises he affirmative, the conclusion will he
affrmative (by Ax. 1).
" Rule 3. — If hoth premises he negative, nothing follows : because
of things mutually agreeing and mutually disagreeing, both may
be different from a third thing (by Ax. 3, 4).
" Two Rules regard the Quantity of Terms.
" Rule 4. — Let the middle he once at least distributed, or taken
APPENDIX. 323
universally ; for the common term frequently contains two or more
species mutually opposed, of which it may be predicated according
to various parts of its extension ; these [specific] terms do not,
therefore, truly agree in one third, unless one at least of them
agrees with the whole middle (by Ax. 3, 4).
" Eule 5. — No term ought to he taken more universally in the
conclusion than in the premises : because no consequence is valid
from the particular to the universal. [Because we should, in that
case, transcend the agreement or disagreement of the two terms
in a third, on which, ex hypothesi, we found].
" [In like manner there are two rules] concerning the Quantity
of Propositions.
"Rule 6. — If one of the premises he particular^ the conclusion
will also he particular.
" Por, Case I. — If the conclusion be affirmative, therefore both
premises will be affirmative (by Rule 1). But, in a particular pro-
position, there is no term distributed ; the middle is, therefore, to
be distributed in one or other of the premises (by Rule 4). It will,
therefore, be the subject of a universal affirmative proposition ;
but the other extreme is also taken particularly, when it is the
predicate of an affirmative proposition, the conclusion will, there-
fore, be particular (by Rule 5).
" Case 2. — Let the conclusion be negative ; its jDredicate is,
therefore, distributed : hence, in the premises, the major and the
middle terms are to be distributed (by Rules 5 and 4).
" But when one of the premises is negative, the other is affirma-
tive (by Rule 3). If one premise be particular, these two terms only
can be distributed ; since one premise affirms, whilst the other is
particular. The minor extreme, the subject of the conclusion, is
not, therefore, distributed in the premises ; it cannot, therefore, (by
Rule 5), be distributed in the conclusion.
"Rule?. — From two particular premises nothing folloius ; at
least according to the accustomed mode of speaking, where the pre-
dicate of a negative proposition is understood to be distributed.
For, l"". If the conclusion affirm, both premises will affirm, and,
consequently, no term is distributed in the premises ; contrary to
^ule 4. 2°, Let the conclusion be negative, its predicate is there-
fore distributed ; but in particular premises there is only distributed
324
APPENDIX.
the predicate of a negative proposition ; there is, therefore, neces-
sarily a vice, (either against Kule 4 or Rule 5)." a
VI. — Savonaeola.
Savonarola, Compendium Logices, L. iv. p. 115, ed. Venetiis,
1542. — " In whatever syllogism any j^roposition can be concluded,
there may also be concluded every other proposition which follows
out from it." On this he remarks : "When any syllogism infers a
conclusion flowing from its immediate conclusion, it is not to be
called one syllogism but two. For that other conclusion does not
follow simply in virtue of the premises, but in virtue of them
there first follows the proper conclusion, and from this conclusion
there follows, by another syllogism, the conclusion consequent on it.
Hence there are tacitly two syllogisms ; otherwise the moods of
syllogisms would be almost infinite."
VII. — Baumgarten.
Baumgarten, Acroasis Logica. Ed. Tollner. Ed. I. 1765,
§ 297. " Every reasoning depends on this proposition : — A and
B connected with a third C, are connected with each other : in
affirmation immediately, in negation mediately. This proposition
is, therefore, the foundation and principle of all reasoning ; which,
however, is subordinate to the principle of Contradiction.
§ 824. " Every ordinary syllogism concluding according to the
a " Rules 1 and 7 are thus contracted
into one : The conclusion follows the
weaker j)art ; that is, the negative or
the particular. All these Rules are in-
cluded in the following verses :
Distribuas medium, nee quartus ter-
minus adsit,
Utraque nee prtemissa negans, nee
particularis.
Sectetur partem conclusio deterio-
rem ;
Et non distribuat nisi cum in-cemissa,
negetve.
In an unusual mode of speaking, a cer-
tain negative conclusion may be effected
with a non-distributive predicate. As
in this exam file
A B
Some Frenchmen are [some] learned ;
C B
Some Englishmen are not [any] learned,
Therefore, some Englishmen are not some
Frenchmen."
(What are within [ ] are by me).
[Written Autumn 1844. In the latest
notation (,) is substituted for (.), and (:)
for (:.). See below, Appendix XI. — Ed]
APPENDIX. 325
Dictum, either de Omni, or de Nidlo. This Dictum is thus the
foundation of all ordinary syllogisms," (It had been previously
announced, §§ 319, 321.)
"Whatever is truly affirmed of a notion universally, is also truly
affirmed of all that is contained under it. Whatever is truly
denied of a notion universally, is also truly denied of all that is
contained under it."
VIII.— Eeimaeus.
Eeimarus, Vernunftlehre. 1766.
§ 176. " The fundamental rules of syllogism are, consequently,
no other than the rules of Agreement [Identity] and of Contradic-
tion. For what the geometer in regard to magnitudes takes as
the rule of equality or inequality, that the reasoner here adopts as
the universal rule of all mediate insight : — If two things he iden-
tical with a third, they are also in so far identical with each
other. But if the one he, and the other he not, identical with the
third, then they are not 'mutually identical, hut rather mutually
repugnant."
§ 177. Here he notices that the Dictum de Omni et Nullo is
not properly a rule for all figures, but for the first alone,
IX. — Waldin,
Waldin, Novum Logicce Systema. 1766.
§ 335. " Since the syllogism requires essentially nothing but a
distinct cognition of the sufficient reason of some proposition, the
most universal rule of all syllogisms is, — Tlie sufficient reason of a
given proposition is to he distinctly cognised.
§ 364. " The most general rule of all reasonings, (§ 335), remains
also the rule of all reasonings as well in synthesis as in analysis.
But in the synthesis of the ordinary syllogism, the middle term in
the major proposition is referred to the major term, in the minor
proposition to the mmor term. (§ 360). Wherefore, from this
relation we must judge whether the middle term be or be not the
sufficient reason of the conclusion. Wherefore, the synthesis of the
ordinary syllogism is to be cognised from the relation of its ideas.
This you may thus express :
" 1,) After the true projwsition, the relation of whose ex-
tremes you distinctly apprehend ;
326 APPENDIX.
" 2.) Add to its subject or iDvedicate another idea different
from both, whether agreeing or disagreeing ;
" 3.) Inquire into the relation of the added idea, to the end
that you mau knoiv whether the middle term in the given relation
infer the conclusion; and this is known by tlie application of the
rules of Reciprocation, Subordination, Go-ordination, and Oppo-
sition. If any one wish to call this the Dictum de Omni et Nullo,
I have no objections."
" Observation. This they call the Dictum de Omni et Nullo of
the celebrated Rensch. It stands true indeed ; but is beset with diffi-
culties, inasmuch as it is rather a complesus of all rules than one
only, which as yet is to be referred to the class of pia desideria.
Logicians have, indeed, taken pains to discover one supreme rule
of all ordinary reasonings ; but no one has as yet been so happy
as to find it out." Then follows a criticism of the attempts by the
Port Royal and Syrbius.
X. — Stattlee.
Stattler, Philosophia, P. I, Logica, 1769.
§ 237. " In this comparison of two ideas with a third, six
different cases may in all occur : for either,
1.) " One of the two ideas contains that same third, which
again contains the other ; or,
2.) " Both of the two are contained in the third ; or,
3.) " Each of the two contains the third ; or,
4.) " One of the two contains the third, the other being repug-
nant with it ; or,
5.) " One of the two is contained in the third, luith luhich the
other is repugnant ; or,
6.) Both of the two are repugnant to the third.
" The former three cases generate an affirmative conclusion, the
latter three a negative." In a note Stattler eliminates a seventh case,
in which neither may contain, and neither be repugnant to the
third.
§ 244. General Law of all Reasonings. '' In all reasonings,
as often as a consequent is, by legitimate form, inferred from
an antecedent, so often is there included in the antecedent what
the consequent enounces ; cither the congruity and reciprocal
APPENDIX. 827
containment, or the 7'epugnance of A and 0; and if such be not
included in one or other of the antecedents, whatever is inferred
in the consequent is void of legitimate form."
XI. — SautePw
Sauter, Institutiones Logicce, 1798.
§ 123. " Foundatiojis of Syllogism. — In every syllogism there
are two notions compared with a third, to the end that it may
appear whether they are to be conjoined or sejoined. There are,
therefore, here, three possible cases. For there agree with the
assumed third, either both notions, or one, or neither. In reasoning,
our mind, therefore, reposes on these axioms, as on fundamental
principles.
].) " Wliere two notions agree with the same third, they agree
with one anotJter.
2.) " Where one is contained by the third, luith luhich the other
is repugnantj they are mutually repugnant.
3.) " When neither notions agrees with the third, there is between
them neither agreement nor repugnance."
XII. — SUTER.
Suter, Logica.
§ 61. " Quae eidem tertio conveniunt vel disconveniunt, etiam
conveniunt vel disconveniunt inter se."
XIII.— Seguy.
Seguy, Philosophia ad Usum Scholarum Accommodata, T. I.
Logica. Paris, 1771.
P. 175, ed. 1785. " Concerning the rule of recent philoso-
phers."
Having recited the general rule of the Port Royal Logic, he
thus comments on it : —
" 1°, This is nothing else than the principle of reasoning ; there-
fore, it is improperly adduced as a new discovery, or a rule strictly
so called.
" 2°, It may be useful, to the rude and inexperienced, to recog-
nise whether a syllogism be legitimate or illicit.
" But the principal fault of this rule is, that it contains no certain
method whereby we may know when, and when not, one of the
328 APPENDIX.
premises contains a conclusion ; for the discovery of which we
must frequently recur to the general rules.""
P. 178. Seguy exposes Father Buffier's error in saying "that,
according to Aristotle and the common rules of Logic, the middle
term ought absolutely to be the predicate in the first or major
proposition ;" seeing that the middle term is not the predicate in
the first and third Figures. This must be a mistake ; for I can-
not find such a doctrine in Buffier, who in this respect, in many
places, teaches the correct.
XI v.— HOFFBAUEE.
Hoffbauer, Anfangsgrilnde der Logik, ITO^, 1810.
"§317. Fundamental Principles.
" I. 1.) An attribute which belongs to all and every of the objects
contained under a notion, may also be aflSrmed of these objects so
contained. (Dictum de Omni.)
" 2.) An attribute which belongs to none of the objects contained
under a notion, must also be denied of these objects so contained.
(Dictum de Nulla)
" II. When, of the objects X and Z, the one contains an atttri-
bute which the other does not contain, and they are thus different
from each other, then X is not Z, and Z is not X.
" III. 1.) When objects which are contained under a notion a are
also contained under another notion h, then this last notion con-
tains under it some at least of the objects which are contained
under the first.
" 2.) If certain objects which are not contained under a notion a
are contained under h, then 6 contains under it some at least of
the objects which are not contained under a.
" IV. 1.) If objects which are contained under a notion a belong
o Followed by Tjarroque, Elemens de E contra, PhilosopJiia Lugdunensis, i.
Philosophie, p. 231 ; Galluppi, Ze2/or^^ rfj 159. Troxler, Logik,\l 41.
Logica e di Metafisica, 1. 47, i. 348.
APPENDIX. 329
to those which are contained under another notion h, tlien this
second notion b contains under it some at least of the objects
which are contained under a.
" 2.) If all objects which are contained under a notion a belong
to those which are not contained under a certain other notioii b,
then this notion b contains under it no object w^hich is contained
under the notion a.
" 3.) If all the objects contained under a certain notion a are
different from certain other objects contained under b, then b con-
tains under it at least some objects which are not contained
under a.
XV.— Kant.
Kant, Logik 1800-6. II. Syllogisms.
" § 56. Syllogism in general. — A syllogism is the cognition that
a certain proposition is necessary, through the subsumption of its
condition under a given general rule.
" § 57. General principle of all Syllogisms. — The general
principle whereon the validity of all inference, through the
reason, rests, may be determinately enounced in the following
formula : —
" What stands under the condition of a rule, that stands also
under the rule itself
" Observation. — The syllogism premises a General Ride, and a
Sid)Sumption under its Condition. Hereby we understand the con-
clusion a priori, not as manifested in things individual, but as
universally maintained, and as necessary under a certain condition.
And this, that all stands under the universal, and is determinable
in universal laws, is the Principle HhqM oi Rationality ov oi Neces-
sity, (principium rationalitatis sen necessitatis)
" § 58. Essential constituents of the Syllogism. — To every syl-
logism there belong the three following parts : —
"1.) A general rule, styled ih^Q Major proposition, (pivjwsitio
major, Obersatz)
" 2.) The proposition which subsumes a cognition under the con-
dition of the general rule, called the Minor proposition, {propositio
minor, Untersatz) ; and, finally,
" 8.) The proposition which affirms or denies the predicate in the
330 APPENDIX.
rule of the subsumed cognition, — the Concluding proposition,, or
Conclusion, {Gonclusio, tichlasssatz).
" The two first propositions, taken in connection with each other,
are called the Antecedents, or Premises, ( Voi'dersdtze).
" Observation. — A rule is the assertion of a general condition.
The relation of the condition to the assertion, how, to wit, this
stands under that, is the Exponent of the rule. The cognition,
that the condition, (somewhere or other), takes place, is the Suh-
sumption.
" The nexus of what is subsumed under the condition, with the
assertion of the rule, is the Conclusion."
Having shown the distribution of syllogisms into Categorical,
Hypothetical, and Disjunctive, he proceeds to speak of the first
class.
" § 63. Principle of Categorical Syllogisms. — The principle
whereon the possibility and validity of Categorical Syllogisms
is this, — ^What pertains to the attribute of a thing, that pertains to
the thing itself ; and what is repugnant to the attribute of a thing,
that is repugnant to the thing itself, {Nota notce est nota rei ipsius;
Repugnans notce, repugnat rei ipsi).
" Observation. — From this principle, the so-called Dictum de Omni
et Nullo is easily deduced, and cannot, therefore, be regarded as the
highest principle either of the Syllogism in general, or of the Cate-
gorical Syllogism in particular. Ge7ieric and Specific Notions are
in fact the general notes or attributes of all the things which stand
under these notions. Consequently the rule is here valid — What
pertains or is repugnant to the genus or species, that also per-
tains or is repugnant to all the objects which are contained
under that genus or species. And this very ride it is which is
called the Dictum de Omni et Nullo."
XVI.— Cheistian Weiss.
Christian Weiss, Logik, 1801.
"§ 216. Principle for all Syllogisms. — The principle of every
perfect Syllogism consists in the relation of one of the notions
contained in the conclusion to a third notion [terminus medius),
to which the other notion of the conclusion belongs. Noiu the re-
lation ivhich tJte first of these holds to the middle notion, the
APPENDIX. 831
same r>iust hold to the second, just because the second coin-
cides with the middle notion to the same extent as the first.
'-' Remark. — 'Relation to' means only any determinately
thought relation, expressed in a judgment
" The older logicians adopt, some of them, the principle Nota
notcB est notarei ipsius, — quod rejjugnat notes, repugned ipsirei ;
this, however, is only properly applicable to the first figure. The
expression of others is preferable, Queecumque conveniunt {vet
dissentiunt) in uno tertio, eadem conveniun (vel dissentiunt) inter
se. Others, in fine, among whom is Wolf, give the Dictum de
Omni et Nullo (cf § 233) as the princij)le of syllogisms in gene-
ral ; compare Philosophical Aphorisms [of Platner], P, i. § 54^6.
All inference takes place according to a universal rule of reason,
here only expressed in reference to syllogism, to which, however,
some have chosen to give a more mathematical expression ; — If
two notions be equed to a third, they arc also equed to eeich other.
[]\^ota bene. — Weiss's mistake (§ 231) in supposing that Aris-
totle " designated the syllogistic moods with words, like his learned
followers."]
" § 231. Categorical Syllogisms, Figure I. — The first figure con-
cludes by means of a subordination of the minor term in the
conclusion under the subject of another judgment.
" § 233. This takes place under the general principle : —
" 1.) What pertains to edl objects conteiined under a notion,
that pertains edso to some and to each individual of their num-
ber among them.
"2.) What belongs to none of the objects contained under a
notion, that also does not pertain to some or to any individual of
their number among them.
" These are the celebrated Dicta de Omni and de Nidlo, — Quid-
quid preedicatur de onini, idem etiam de ediquo, and, Quielquid
prcedicatur de nullo, id nee de cdiequo proedicatur."
XVII.— Fries.
Fries, System der Logik.
" § 52. Hitherto we have maintained two views of the Syllogism
in connection. The end in view of reasoning is this, — that cases
should be subordinated to general rules, and through them become
determined. For example, the general law of the mutual attrac-
332 APPENDIX.
tion of all heavenly bodies has its Avhole significance, for my
knowledge, in this, that there are given individnal heavenly
bodies, as Sun and Earth, to which I apply it. To enoimce these
relations, it is, in the first place, necessary that I have a general rule,
as Major Proposition, (Obersatz) ; in the second, a Minor Propo-
sition, (Untersatz), which subordinates cases to the rule, and,
finally, a Concluding Proposition, which determines the cases
through the rule. On the other hand, we see that every Con-
clusion is an analytico-hypothetic judgment, and this always
flows from the Dictum de Omni et Nullo, inasmuch as the relation
of subordination of particular under universal notions, is the only
relation of Reason and Consequent given in the form of thought
itself. Now, if the conclusion, as syllogism, combines a plurality
of judgments in its premises, in this case the principle of the in-
ference must lie in a connection of the thoughts, — a connection
which is determined by the matter of these judgments. In the
simplest case, when taking into account only a single syllogism,
I thus would recognise in the premises the relation of subordina-
tion between two notions by reference to the same third notion,
and therethrough jjcrceive in the conclusion the relation of these
two notions to each other. I know, for example, that all men
are infiortal, and that Gains is a man. Consequently, through the
relation of the notion of moi^tality, and of my imagination of
Caius, to the notion man, the relation of Caius to mortaliti/ is
likewise determined : — Caius is mortal. The first of these views
is a mere postulate ; but in conformity to the second we are
enabled immediately to evolve the general form of syllogisms, and
from this evolution does it then become manifest that all possible
syllogisms satisfy the postulate. We, therefore, in the first instance,
attach ourselves to the second view. Through this there is deter-
mined as follows : —
" 1.) Here the determination of one notion is carried over to an-
other, superordinate or subordinate to itself. To every syllogism
there belong three notions, called its tei'ms, (termini). (We say
notions, (Begriffe), because they are, in general, such, and when indi-
vidual representations [or images] appear as terms, in that case
there is no inter- commutation possible). A major term, or supe-
rior notion, {Oberhegriff), P, is given as the logical determination
of a middle term or notion, (Mittelbegriff), M, and, through this,
APPENDIX. 333
it is positively or negatively stated as the determination of a minor
term or notion, {Unterhegriff), S.
" 2.) If, then, we regard the propositions in which these relations
are enounced ; there is, firstly, in the conclusion, [Schlusssatz],
the minor term, or inferior notion, subordinated to the major term,
or superior notion, (S is P). Further, in one of the premises, the
middle must be connected with the major term or notion, (M is P).
This is called the major proposition, {Ohei^satz). In the other,
again, the minor is connected with the major term or notion, (S is
M) ; this is called the minor 2')roposition, {Untersatz).
"The form of every syllogism is therefore : —
Major Proposition, M is P.
Minor Proposition, S is M.
Conclusion, S is P.
" In the example given above, man is the middle term ; moHality
the major term ; and Caius the minor term. The syllogism is : —
Major Proposition, All men are mortal ;
Minor Proposition, Caius is a man ;
Conclusion, Caius is mortal.
" The fundamental relation in all syllogisms is that of the
middle term to the major and minor terms, in other words, that of
the carrying over of a logical determination from one notion to
another, through certain given subordinations. Tor howbeit the
Dictum de Omni et Nullo, as a common principle of all syllogisms
in the formula, — What liolds good of the universal, holds also good
of the particulars subordinate thereto, and still more in that
other, — The attribute of the atti^ibute is also the attribute of the
thing itself, — is proximately only applicable to the categorical sub-
ordination of a representation [or notion] under a notion ; stiU,
however, the law of mental connection is altogether the same in
syllogisms determined by the subordination of consequence under
a reason, [Hypothetic Syllogisms], or of the complement of parts
under a logical whole, [Disjunctive Syllogisms]. The displayed
form is the form of every possible syllogism. In fact, it also coin-
334 APPENDIX.
cides with the first requirement that, in the syllogism, a case
should always be determined by a rule, inasmuch as every syllo-
gism proposes a universal premise, in order rigorously to infer its
conclusion. This will be more definitely shown, when we treat of
syllogisms in detail. Only the declaration, tliat the rule is always
the major 'proposition, is sometimes at variance with the declara-
tion, that the major proposition contains the relation of the
middle term to the major term. We must, however, in the first
place, always follow the determination of the latter. For every
syllogism properly contains the three processes: — 1). The subor-
dination of a particular under a universal ; this is the function of
the minor proposition, and the relation between the minor and major
terms ; 2), Postulate of a logical determination for one of these
two ; this is the function of the major jjroposition, and the relation
of the middle to the major term ; 3), The carrying over this deter-
mination to that other ; this is the function of the conclusion and
the relation of the minor to the major term.
" § 53. The subordination of a particular to a universal must,
therefore, in every syllogism, be understood wholly in general.
Here either a particular may be determined through its superordi-
nated universal, and such an inference from universal to particular
we shall call a syllogism in the first figure ; or there is a universal
known through its subordinated particular, and this inference from
the particular to the universal is called a syllogism in the second
\third^ figure. If, for example, the subordination is given me, —
A II gold is metal ; I can either transfer an attribute of metal,
for instance fusibility, to the gold, or enounce an attribute of
gold, ductility, for instance, of some metal. In the first case, I
draw a conclusion in the first figure, from the universal to the
particular : —
A II metal is fusible ;
All gold is metal ;
All gold is fusible.
" In the other case, I conclude in the second [third] figure from
the particular to the general : —
All gold is ductile ;
A II gold is metal ;
Some Tnetal is dtictile."
APPENDIX. 835
Then, after distribution of the Syllogism into Categorical, Hypo-
thetical, and Divisive, (Disjunctive), he proceeds with the first
class.
XVIII. — KlESEWETTER.
Kiesewetter, AUgemeine Logik, 1801, 1824*. I. Theil.
"§ 228. — All pure Categorical Syllogisms, whose conclusion is an
affirmative judgment, rest on the following principle : — What j^ei--
tains to the attribute of an object, j^ertains to the object itself. All
syllogisms, whose conclusion is a negative judgment, are based upon
the principle : — What is repugnant to the attributes of an object,
is repugnant to the object itself. Two principles which can be
easily deduced, — the first from the principle of Identity, the second
from the principle of Contradiction.
" § 229. — If we take into consideration that the major proposi-
tion of every categorical syllogism must be a universal rule, — from
this there flow the following rules : —
"1. Whatever is universally affirmed of a notion, that is also
affirmed of everything contained under it. The Dictum de Omni.
" 2. Wliat is universally denied of a notion is denied also of every-
thing contained under it. The Dictum de Nullo.
" These rules are also thus exj)ressed : —
" What pertains to the genus or species, j)ertains also to whatever
is contained under them. What is repugnant to the genus or
species, is repugnant also to whatever is contained under them."
See also the Weitere Auseinandersetzung on the paragraphs,
XIX. — Laeroque.
Larroque, EUmens de Philosophic, Paris, 1830. Logique,
Ch. i., p. 202. " The attribute of an affirmative proposition is
taken sometimes particularly, sometimes universally. It is taken
particularly, when it has a greater extension than the subject ; uni-
versally, when it has not a greater extension, which occurs in every
proposition where the two terms are identical. The reason of this
diff'erence is palpable. If the attribute be a term more general
than the subject, we affirm that the subject is a species or indivi-
dual contained in the extension of the attribute : — Man is mortal ;
Paul is learned : — that is, man is one, and not the only, species
S36 APPENDIX.
contained in the extension of the term mortal ; Paul is an indivi-
dual, and not every individual, contained in the extension of the
term learned. If, on the contrary, the attribute be not more
general than the subject, the attribute is the same thing with the
subject, and, consequently, we affirm that the subject is all that is
contained in the extension of the attribute : — A circle is a plane
surface, which has all the points, in [a line called] its circumfer-
ence, at an equal distance from a j)oint called its centre — that is,
a circle is all or every plane surface, &c.
" The attribute of a negative proposition is always taken univer-
sally. When we deny an attribute of a subject, we deny of this
subject everything that has the nature of that attribute, that is to
say, all the species, as all the individuals, contained in its extension :
The soul is not extended ; to wit the soul is not any of the species,
not any of the individuals contained in the extension of the term
extended."
Ch. ii., p. 230. "We have supposed, in the demonstration of
these rules [the general rules of the Categorical Syllogism], that
the attribute of an affirmative premise is always taken particularly.
It would, therefore, seem that the calculations on which this demon-
stration rests, are erroneous, whensoever the attribute is not a term
more general than the subject, for we have seen that, in these cases,
the attribute can be taken universally. But it is to be observed, tliat
when the two terms of a proposition are identical, if the one or the
other may be taken universally, they cannot both be so taken at
once ; and that, if it be the attribute which is taken universally, it
ought to be substituted for the subject, which then affords a parti-
cular attribute. A triangle is a figure which has three sides and
three angles. We cannot say, A II triangle is all figure, which, &c. ;
but we can say, A II triangle is some figure, which, &c. ; or, A II figure
which has three sides and three angles, is some triangle. Now, in
adopting either of these last expressions of the proposition, the
attribute is particular."
Ch. ii., p. 231. "We have seen that the Syllogism inferred from
its premises a proposition to be proved ; now this conclusion can-
not be inferred from, unless it be contained in, the premises. From
this incontestable observation, the author of the Port Eoyal Logic
APPENDIX. 837
has endeavoured to draw the following pretended rule, by aid of
which we may detect the vice of any fallacious reasoning whatso-
ever : Thus, should one of the premises contain the conclusion^
and the other shoiu that it is so contained. A great many treatises
on Logic call this the single ride of the moderns. This pompous
denomination seems to point at some marvellous discovery, of
which the ancients had no conception, — at some consummative
result of the efforts of the human intellect. It is true, indeed, that
a syllogism is invalid, if the conclusion be not contained in the
premises ; but a fine discovery forsooth ! This all the world
already knew, — Aristotle among the rest ; but he justly noted that
it is not always easy to see whether the conclusion be contained
in the premises, and it is to assure ourselves of this that he laid
down his rules. The pretended rule of the Port Royal is, therefore,
not one at all ; it enounces only an observation, true but barren."
XX. — Galluppi.
Galluppi, Lezioni di Logica e di Metajisica. 1832. Lez.
xlvii., p. 353, ed. 1841.
" In a reasoning there must be an idea, common to the two pre-
mises ; and a judgment which affirms the identity, either partial
or perfect, of the other two ideas."
In the same Lecture, (p. 348), he shows that he is ignorant of the
law quoted from the Philosophia Lugdunensis, being by the
authors of the L'Art de Penser.
XXI. — BUFFIER.
Buffier, Premiere Logique, about 1725. The following is from
the Recapitulation, § 1 09 : —
The Syllogism is defined, a tissue of three propositions so con-
stituted, that if the two former be true, it is impossible but that
the third should be true also. (§ 62.)
The first Proposition is called the Major ; the second the
Minor ; the third the Conclusion, which last is the essential end
in view of the syllogism. (§ 65.)
Its art consists in causing a consciousness, that in the conclusion
the idea of the subject comprises the idea of the predicate ; and
this is done by means of a third idea, called the Middle Term,
(because it is intermediate between the subject and predicate), in
VOL. II. Y
838 APPENDIX.
such sort that it is comprised in the subject, and comprises the pre-
dicate. (§ 67.)
If the first thing comprise a second, in which a third is comprised,
the first comprises the third. If a fluid comprise chocolate, in
which cocoa is comprised, the fluid itself comprises cocoa. (§ 68.)
To reach distant conclusions, there is required a plurality of
syllogisms. (§ 71.)
Our rule of itself suffices for all syllogisms ; even for the nega-
tive ; for every negative syllogism is equivalent to an affirmative.
(§77.)
Hypothetical syllogisms consist in the enouncement by the
major premise, that a proposition is true, in case there be found a
certain condition ; and the minor premise shows that this condition
is actually found. (§ 79.)
Disjunctive syllogisms, to admit of an easy verification, ought to
be reduced to hypotheticals. (§ 81.)
Although the single rule, which is proposed for all syllogisms, be
subject to certain changes of expression, it is nevertheless always
the most easy ; in fact, all logical laws necessarily suppose this
condition. (§ 87.)
The employment of Grammar is essential for the practice of
Logic. (§ 90.)
By means of such practice, which enables us to estimate accu-
rately the value of the terms in every proposition, we shall likewise
obtain the rule for the discovery of all sophisms, which consist only
of the mere equivocation of words, and of the ambiguity of propo-
sitions. (§ 92 et seq.)
XXII.— VlCTORIN.
Victorin, Keue naturlichere Darstellung der Lo<jik,Yienvia.,18S5.
II. Simple Categorical Syllogisms. § 04. The fundamental rule
of all such syllogisms : —
" In what relation a concept stands to one of two reci-
procally subordinate concepts, in the same relation does it
stand to the other."
§ 91^. First Figure ; fundamental rule : — " As a notion deter-
7nines the higher notion, so does it determine the lower of the
same ;" or, " In tuhat relation a notion stands to one notion, in
the same relation it stands to the loiuer of the same."
APPENDIX. 339
§ 96. Second Figure ; fundamental rule : — " Whentiuo notions
are ojypositely determined hy a third notion, they are also them-
selves opposed ;" or, " If two notions stand to a third in op-
posed relations, they also themselves stand in a relation of
opposition."
§ 98. Third Figure ; fundamental rule : — " As a notion deter-
mines the one of two [^o lY] subordinate notions, so does it de-
termine the other ;" or, " In what relation a notion stands to the
one of two \to if] subordinate notions, in the same relation stands
it also to the other."
§ 100. Fourth Figure ; fundamental rule : — " As a notion is
determined by the oneoftiuo subordinate notions^ [tivo notions in
the relation to each other of subordination^ so does it determine
the other;" or, "In what relation one of two subordinated notions,
[notions reciprocaUy std)ordinate or superordinate], stands as to
a third, in the same relation stands it also to the other."
[b) Fundamental Laws of Syllogism. — Eefeeences.
(See Galluppi, Lezioni di Logica e di Metafisica, Lez. xlvii.,
vol. i. p. 345 d seq. ; Troxler, logik, i. p. 33 ; Bolzano, Wissens-
chaftslehre, logik, vol. ii. § 263, p. 543.)
I. Logicians who confound the Nota notfe and the Dictum de
Omni, being ignorant of their several significances ; making them —
a) Co-ordinate laws without distinction.
Jager, Handb. d. Logik, § 68, (1839) ; Prochazka, Gesetjzb.,
fd.,Denken,% 217, (1842) ;'Calker, Denklehre, § 143, (1822).
Troxler, Logik, ii. p. 40.
b) Derivative ; the Dictum de Omni, to wit, from the Nota
notte. This supreme or categorical.
Wenzel, Elem. Philos. Log.., §§ 253, 256. Canonik, § 64.
Kant, Diefalsche Spitzf, § 3. Logik, § 63. Krug, Logik, § 70.
Bachmann, Logik, § 123. Jakob, Logik, § 262, 4th ed. 1800 ; 1st
ed. 1788.
II. Logicians who enounce the law of Identity, (Proportion,) in
the same third, by the mathematical expression Equality.
Reimarus, Vernunftlehre, § 176. Mayer, Vernunftschlusse,
i. p. 290. Arriaga, In. Sum., D. III. § 3, p. 23.
III. Logicians who make the Dictum de Omni the fundamental
rule of syllogisms in general.
310 APPENDIX.
Aristot., An. Prior., L. i. c. 1, § 4 Wolf, PJiil. Rat, § 853.
Schcibler, Op. P. iv. De Si/ll c. ii. § 12. Jac. Thomasius, Erot
Log., c. 395. Buttner, Cursus Philos., Log., § 146. Conimbri-
censes, Ln Arist. Dial., An. Prior., L. i. c. 2, p. 204.
IV. Logicians wlio confound or make co-ordinate the law of
Proportion or Analogy, and the Dictum de Omni.
Wyttenbach, Prcec. Philos. Log., P. iii. c. 6, § 4. Whately, Logic,
Intr., ch. II. p. iii., § 2. Leechman, Logic, P. III. eh. 2. Kecker-
mann, Sy sterna Logicoe Minus, L. iii. c. 2. Syst. Log. Majus.,
L. iii. c. 5.
V. Logicians who make the Law of Identity the one supreme.
Suter, Logica, § 61, calls this the principle of Identity and Con-
tradiction. Aldrich, Comp. L. i. c. 3, § 2, p. 2. Hutcheson, Log.
Comp.,V. iii. c. 2. Arriaga, Gur. Phil., Ln. Sum., D. iii. §§ 16-22,
pp. 23, 24. Larroque, Logique, p. 224. Mayer, Vernunftschlusse,\.
p. 293. Troxler, Logik, ii. pp. 33, 40. Eeimarus, Vernunftlehre,
§ 176. Mendoza, Disp. Log. et Met., I. p. 470. Derodon, Log.
Rest., De Log. pp. 639, 644. Darjes, Via., &c., § 271, p. 07. Smigle-
cius, Logica, D. xiii. p. 517. qu, &c. Fran. Bonae Spei, Com.
Prim, in Log. Arist., D. vii. d. 2, p. 25. Cursus Complut, De
Arg., L. iii. c. 4, p. 57. Alstedius, Lnc, Logica, § ii. c. ]0, p. 435.
Havichorst, Lnst. Log., § 323. Poncius, Cursus Philos. Ln An.
Pi'ior., D. XX. qu. 5, p. 282.
VI. Logicians who restrict the Dictum de Omni to the first
Figure (immediately).
Aldrich, Comp. 1. 1, c. 3, § 7. Noldius, Log. Rec, c. xii. p.
290. Grosser, Pharus LnteUectus, § iii. p. 1, memb. iii. p. 137.
VII. Logicians who make the Dicta de Omni et NuUo the
supreme canons for Universal Syllogisms ; the law of Proportion for
Singular Syllogisms.
Burgersdicius, Lnst. Log., L. ii. c. 8, p. 171. Melancthon,
Erot. Dial, De Syll. Expos., L. iii. p. 172, ed. 1586. Fonseca,
Lnstit. Dial, L. vi. cc. 21, 24, pp. 363, 373.
VIII. • What name given by what logicians to the Law of Pro-
i:)ortion, &c.
Law of Proportion, or of Analogy, Keckermann, Syst. Log.,
L. iii. c. 5, Op., p. 746. Alstedius, Encycl.., p. 435, to ava\oyia<;.
Dictum de Omni et Nulla Majus, Noldius, Log., p. 288. Of
Ldentity, Zedler's Lex. Pr. convenientim, Darjes, Via ad Verit, §
270, p. 96. Law of proportional Identity and Non-Identity, Self.
APPENDIX. Oil
IX. Logicians erroneously supposing Aristotle to employ, besides
the Dictum de Omni, the rule of Proportion as a fundamental law
of syllogism.
Kapin, Reflexions sur la Logique, § 4.
X. Terms under which the law of Proportion has been enounced.
Agree ivith. Coincide tuith. The same with. (7o7iere, (Syrbius).
Co-exist (bad). Co-identical with. Equal to, (No. ii.) In com-
bination ivith, Darjes, Via ad Ver. p. 97, (includes negative.)
Convertible.
(c) Enunciations of the Higher Laws of Syllogism.
Law of Proportion.
Aristotle, ElencJi, c. vi. § 8. " Things the same with one and
the same, are the same with one another." Compare Topica, L. vii.,
c. 1, § 6. Thus Scotus, In An. Prior., L. i. qu. 9, £ 2^8.
Some say, "Uni tertio indivisibili" — some others, "Unitertio
indivisibili, iudivisibiliter sumpto." Others, in fine, say, " Uni
tertio, adequate sumpto." See Irenseus, Integ. Philos. Log., §§ 3,
5. Some express it, " Things that are equal to the same third are
equal to each other." See Irena^us, ib. So Reimarus, Mayer.
Some express it, " Qutecunque conveniunt, (vel dissentiunt), in
uno tertio, eadem conveniunt, (vel dissentiunt), inter se."
" Quce duo conveniunt cum uno quodam tertio, eatenus conveni-
unt inter se ; quando autem duorum unum convenit cum tertio,
et alterum huic repugnat, repugnant quoque eatenus sibi invicem,"
Wynpersse, Inst. LogiccB, § 272, Lug. Bat. 3d ed. 1806.
Noldius, {Logica, p. 288), calls these the Dicta de Omni et de
Nullo. The former is, " Qusecunque affirmantur in aliquo tertio,
(singulari identice, universal! et identice et complete distributive),
afl&rmantur inter se." The latter, " Quorum unum [totaliter] affir-
matur in aliquo tertio, alterum negatur, ea inter se negantur."
Noldius.— " Whatever is affirmed essentially of a subject, is
affirmed of all that is inferior or reciprocal to that subject. What-
ever is denied of a subject, is denied of all inferior or reciprocal."'
(See Noldius against the universal application of these Dicta, Log.
Rec. p. 290).
Reusch, {Syst Logicum, ed. i. 1734, § .503) makes the Dicta
de Omni et Nullo the rule of ordinary syllogisms, and thus enunci-
ates them, " Si quid prc^edicatur de omni, illud etiam prredicatur de
aliquo : et, Si quid predicatur de nullo, illud etiam non prsedicatur
342 APPENDIX.
de aliquo. Sensus prions est, Quidquid de genere, vol specie
omni prffidicari potest, illud etiam prsedicatur de quovis sub illo
genere, vel sub ilia specie, coiitento ; Item, — Cuicunque corn-
petit definitio, illi qiioque competit defiiiitum : " (and so vice versa
of the other).
Syrbius gives these two rules : —
1) "If certain ideas cohere with a one-third, they also cohere in
the same manner with each other ; "
2) " Ideas which do not cohere with the same one-third, these do
not cohere with each other." (Given in the original by Waldin,
Systema, p. 162. See also Acta Eruditorum, 1718, p. 833.)
Syrbius things that the law of Proportion, unless limited, is false.
Darjes, Via ad Veritatem, (1755), § 270, p. 96, 2d ed. 1764,
" Two [things or notions] in combination with the same third,
may be combined together in the same respect, (ea ration e), where-
in they stood in combination with that third." (See further ; shows
that other rules are derived from this.)
Dictum de Omni, &c.
Aristotle, Anal. Pr., L. i., c. i., § 11.
" To be predicated, de Omni, universally is, when we can find
nothing under the subject of which the other [that is, the predicate]
may not be said ; and to be predicated de Nullo, in like manner."
Jac. Thomasius, Erotemata Logica, 1670.
" 40. What do you call the foundation of syllogism ? — The Dic-
tum de Omni et Nullo.
" 41, What is the Dictum de Omni ? — When nothing can be sub-
sumed under the subject of the major proposition of which its j)re-
dicate may not be affirmed.
" 42. What is the Dictum de Nullo ? — When nothing can be sub-
sumed under the subject of the major proposition of which its predi-
cate is not denied."
Thomasius notices that the first rule applies only to the affirma-
tive moods of the first figure, Barbara and Darii ; the second only
to the negative moods of the same figure, Celarent and Ferio.
(cZ) Objections to the Dictum de Omni et Nullo.
I. As a principle of syllogism in general.
II. As a principle of the First Figure, as enounced by Aristotle.
1°, Only applies to syllogisms in extension.
APPENDIX. 343
2°, Does not apjDly to individual syllogisms ; as, Peter is run-
ning ; hut some man is Peter ; therefore, some man is running.
(Arriaga, In. Summ., p. 24.)
8°, Does not apply in co-extensive reasonings ; as, All trilateral
is {all) triangular ; hut all triangular has three angles equal to
two right angles ; ergo, &c. Arriaga, ih.
Dictum de Omni et NuUo does not apply,
1°, To the other Figures than the First.
2°, Not to all the moods of First Figure, for in many of these the
higher class is subjected to the lower.
3°, The form of the First Figure does not depend upon the
principle of the Dictum de Omni et Nullo. This imperfect ; not upon
the thoroughgoing principle, that in this figure one notion is com-
pared to a second, and this second with a third.
(1
(3
(4
(5
(6
(1
(3
(5
(6
(1
(2
(3
(4;
(6
(7:
(8:
(e) General Laws of Syllogism in verse.
Partibus ex puris sequitur nil (2) sive negatis.
Si qua praeit partis, sequitur conclusio partis.
Si qua negata prteit, conclusio sitque negata.
Lex generalis erit, medium concludere nescit.«
Univocusque ; (7) triplex ; (8) ac idem terminus esto.3
Distribuas medium ; (2) nee quartus terminus adsit.
Utraque nee pra^missa negans ; (4) nee particularis.
Sectetur partem conclusio deteriorem ;
Et non distribuat nisi cum praemissa, (7) negetve.r
Terminus esto triplex : medius, majorque, minorque:
Latins hunc quam pra3miss8e, conclusio non vult,
Nequaquam medium capiat conclusio oportet.
Aut semel aut iterum medium generaliter esto.
Nil sequitur gemiuis ex particularibus unquam.
Utraque si pra3missa neget, nihil inde sequetur.
Amba3 affirmantes nequeunt generare negantem.
Est parti similis conclusio deteriori. ")
Pejorem sequitur semper conclusio partem, j ^
a, Petrus Hispanus, Summulce. [Tr. ^ Purchot, with variations of Seguy,
iv. c. 3, f. 45 b.— Ed.] Ph. Lugd., Galluppi. [Purchot, Inst.
jS Campanella, Dialect., p. 384. Phil., vol. i., Loyica, P. iii. c. 3, p. 17L
7 Hutcheson, Log. Comp. [P. iii. c. — Ed.]
3, p. S3.— Ed.]
S44? APPENDIX.
(1) Terminus est geminus, mecliumque accedit utriqiie.
(2) Proemissis dicat ne finis plura, caveto.
(3) Aut semel, aut iterum medium genus omne capessat ;
(4) Officiique tenax rationem claudere nolit.
(1) Terminus est triplex. (2) Medium conclusio vitet.
(3) Hoc ex prtemissis altera distribuat.
(4) Si praemissa simul fuit utraque particularis,
{ (5) Aut utrinque negans, nulla sequela venit.
(6) Particulare prseit ? sequitur conclusio partis.
(7) Ponitur ante negans ? Clausula talis erit.
(8) Quod non prascessit, conclusio nulla requirit.«
Turn re, tum sensu, triplex modo terminus esto.
{Argumentari non est ex particulari.
Neque negativis recte concludere si vis.
{Nunquam complecti medium conclusio debet.
Quantum proemisssB, referat conclusio solum,
f Ex falsis falsum verumque aliquando sequetur ;
I Ex veris possunt nil nisi vera sequi.^
(/) Special Laws of Syllogism in veese.
1. Fig. Sit minor affirmans, nee major particularis.
2. Fig. Una negans esto, major vero generalis.
3. Fig. Sit minor affirmans, conclusio particularis.
4- Fig. a) Major ubi affirmat, generalem sume ininorem.
b) Si minor affirmat, conclusio sit specialis.
c) Quando negans modus est, major generalis hab-
etur."/
B. Ceiticism.
(a) Criticism op the Special Laws of Syllogism.
The Special Laws of Syllogism, that is, the rules which govern
the several Figures of Categorical Reasonings, all emerge on the
suspension of the logical postulate, — To be able to state in language
what is operative in thought. They all emerge on the refusal or
a Isendoorn, Logica, L. iii. c. 8, p. 427, jx 210.
8°, (1652). Chauviu and Walcb, Xc.r. i>. y Ubaghs, Logicce Elementa, § 225,
Sijlloij. Saucrucius, Dialectica ad Mentem Doct-
fi Crakauthorpe, Logica, L. iii. c. 15, HubtUis, L. i. c 3, p. 103. Lond. 1673.
APPENDIX. 345
neglect to give to the predicate that quantity in overt expression,
which it possesses in the internal operations of mind. The logi-
cians assert, 1", That in affirmative propositions the predicate
must be always presumed particular or indefinite, though in this
or that proposition it be known and thought as universal or defi-
nite ; and, 2°, That in negative propositions this same predicate
must be always presumed absolutely, {i. e. universally or definitely),
excluded from the sphere of the subject, even though in this or that
proposition it be known and thought as partially, {i. e. particularly
or indefinitely), included therein. The moment, however, that the
said postulate of Logic is obeyed, and we are allowed to quan-
tify the predicate in language, as the predicate is quantified in
thought, the special rules of syllogism disappear, the figures are
all equalised and reduced to unessential modifications ; and while
their moods are multiplied, the doctrine of syllogism itself is
carried up to the simplicity of one short canon. Having already
shown that the general laws of syllogism are all comprised and
expressed in this single canon,« it now only remains to point
out how, on the exclusive doctrine of the logicians, the special
rules became necessary, and how, on the unexclusive doctrine
which is now propounded, they become at once superfluous and
even erroneous. It is perhaps needless to observe, that the follow-
ing rules have reference only to the whole of Extension.
The double rule of the First Figure, that is, the figure in which
the middle term is subject in the sumption, and predicate in the
subsumption, is, — Sit minor affirmans ; nee major particularis.
Here, in the first place, it is prescribed that the minor premise
must be affirmative. The reason is manifest. Because if the minor
premise were negative, the major premise behoved to be affirma-
tive. But in this figure, the predicate of the conclusion is the
predicate of the major premise; but, if affirmative, the predicate of
that premise, on the doctrine of the logicians, is presumed par-
ticular, and as the conclusion following the minor premise is
necessarily negative, a negative proposition thus, contrary to logi-
cal law, has a particular predicate. But if we allow a negative
proposition to have in language, as it may have in thought, a
particular or indefinite predicate, the rule is superseded.
a See above, p. 285, and below, p. 350. — Ed.
34G APPENDIX.
The second mle, or second part of the rule, of this First Figure,
is, that the major premise should be nniversal. The reason of
this is equally apparent. For ■we have seen, that, by the previous
rule, the minor premise could not be negative, in which case
certainly, had it been allowable, the middle term would, as predi-
cate, have been distributed. But whilst it behoved that the middle
term should be once at least distributed, ^or taken universally),
and, as being the subject of the major premise, it could only be
distributed in a universal proposition, the rule, on the hypothesis
of the logicians, was compulsory. But as we have seen that the
former rule is, on our broader ground, inept, and that the middle
term may be universally quantified, as the predicate either of an
affirmative or negative subsumption, it is equally manifest that this
rule is, in Hke manner, redimdant, and even false.
In the Second Figure, that is, the figure in which the middle
term is predicate both in sumption and subsimiption, the special
mle is, — Una negans esto; major vero generalis.
In regard to the first rule, or first half of the rule, — That one
or other of the premises should be negative. — the reason is mani-
fest. For, on the doctrine of the logicians, the predicate of an
affirmative proposition is always presumed to be particular ; con-
sequently, in this figure the middle term can, on their doctrine,
only be distributed, (as distributed at least once it must be , in a
negative judgment But, on our doctrine, on which the predicate
is quantified in language as in thought, this rule is abolished, a
The second rule, or second moiety of the rule, — That the sump-
tion should be always universal, — the reason of this is equally
clear. For the logicians, not considering that both extremes were
in equilibrio in the same whole of extension, and, consequently,
that neither could claim in. either quantity] the place of major or
minor term, and thereby constitute a true major or a true minor
a [For examples from Aristotle of affirm- positions in Second Figure, and does
ative conclusions in the Second Figure, not give the reason why the inference is
see De C(bIo. L. iL, c. 4, § 4, text 23, ibi good or bad in such syllogism. Cf. Am-
Averroes. PTiyi. L. iL, c. 2, § 12, text monius and Philoponus ad. loc An,
23, ihi Averroes ; c. 4, § 8, text 33, ibi Prior, L. ii, c. 22, §§ 7, 8. An. Post.,
ATerroes. Ih.c. 7,§ 1, text 42, S* Aver- L. i, c 6, § 1, cf ibi, Themistius, Pa-
roes. ^n.Po*f,L. i.c. 12,§ 12,text92, cius, ZabareUa. Cf. also Zabarella, De
ibi Arerroes et Pacius. Argues himself, Quarta Fig. SyTl., c x.]
like Caeneus, from two aSSrmatlYe pro-
APPENDIX. 347
premise ; — the logicians, I say, arbitrarily drew one instead of
two direct conclusions, and gave tlie name of major term to tliat
extreme which formed the predicate in that one concltision, and
the name of major premise to that antecedent proposition which
they chose to enounce first. On their doctrine, therefore, the
conclusion and one of the premises being always negative, it
behoved the sumption to be always general, otherwise, contrary to
their doctrine, a negative proposition might have a particular pre-
dicate. On our doctrine, however, this difficulty does not exist,
and the rule is, consequently, superseded.
In the Third Figure, that is, the figure in which the middle
t^rm is subject of both the extremes, the special rule is, — Sit
minor afirmans; conclusio paHicularis.
Here the first half of the rule, — That the minor must not be
negative, — is manifestly determined by the common doctrine.
For, major and minor terms, major and minor propositions, being
in this figure equally arbitrary as in the second , here the stmiprion
behoving to be afiirmative, its predicate, constituting the major
term or predicate of the conclusion, behoved to be particular also.
But the conclusion following the minor premise wotild necessarily
be negative ; and it would have, — ^what a negative proposition is not
allowed on the common doctrine, — an tmdistribute^i predicate.
The second half of the rtde, — That the concltision mtist be
partictilar, — is determined by the doctrine of the logicians, that
the particular antecedent, which they choose to caU the minor
term, should be affirmative. For, in this case, the middle term
being the subject of both premises, the predicate of the subsump-
tion is the minor extreme ; and that, on their doctrine, not being
distributed in an affirmative proposition, it consequently, forms
the undistributed subject of the conclusion. The conclusion,
therefore, having a particular subject, is, on the common doctrine,
a particular proposition. But as. on our doctrine, the predicate
of an affirmative proposition may have an universal quantification,
the reason fails.
(6) Laws of Second Figuee — ADDrnoxAL."
By designating the quantity of the predicate, we can have the
a Wliat follows to page 349 «as an in Ltftnrts (yoL L p. 408), being an ap-
earlj- written interpolation by the auziior plication of the principle of a quantiSed
348 APPENDIX.
middle term, (wliich in this figure is always a predicate), distributed
in an affirmative proposition. Thus : —
AWPisallM;
All Q is S07ne M ;
Therefore, all S is some P.
All the things that are organised are all the things that are endowed
with life ;
But all 2Jlants are some things endoived with life;
Therefore, all plants are some things organised.
This first rule (see above, Vol. I. p. 408) must, therefore, be thus
amplified : — The middle term must be of definite quantity, in
one premise at least, that is, it must either, 1°, Be a singular, —
individual, — concept, and, therefore, identical in both premises ; or,
2°, A universal notion presumptively distributed by negation in
a single premise ; or, 3°, A universal notion expressly distributed
by designation in one or both premises.
But the second rule, which has come down from Aristotle, and
is adopted into every system of Logic, with only one exception, an
ancient scholiast, is altogether erroneous. For, 1°, There is pro-
perly no sumption and subsumption in this figure ; for the
premises contain quantities which do not stand to each other in
any reciprocal relation of greater or less. Each premise may,
therefore, stand first. The rule ought to be, " One premise must be
definite ; " but such a rule would be idle ; for what is here given
as a special canon of this figure, was aheady given as one of the
laws of syllogism in general. 2°, The error in the principle is
supported by an error in the illustration. In both the syllogisms
given," the conclusion drawm is not that which the premises war-
rant. Take the first or affirmative example. The conclusion here
ought to have been. No S is some P, or Some P is no S ; for
there are always two equivalent conclusions in this figure. In
the concrete example, tlie legitimate conclusions, as necessitated
by the premises, are, — No horse is some animal, and, Soryie
animal is no horse. This is shoAvn by my mode of explicating
predicate tu syllogism. The interpola- probably given still earlier. — Ed,
tion appears in students' notes of the a See above, vol. i. p. 409. — Ed.
Lectures of session 1841-42 ; and was
APPENDIX. 349
the quantity of the predicate, — combined with my symbolical
notation. In like manner, in the second or negative syllogism, the
conclusion ought to have been either of the two following : In the
abstract formula, — All S are not some P ; or. Some P are not all
S ; — in the concrete example, All topazes are not some minerals,
i. e., No topazes are some minerals; or, Some minerals are not
all topazes, i. e., Some miney^als are no topazes.
The moods Cesare and Camestres may be viewed as really one,
for they are only the same syllogism, with premises placed first or
second, as is always allowable in this [Figure], and one of the two
conclusions, which are always legitimately consequential, assigned
to each.
A syllogism in the mood Festino, admits of either premise being
placed first ; it ought, therefore, to have had another mood for its
pendant, with the affirmative premise first, the negative premise
second, if we are to distinguish moods in this figure by the acci-
dental arrangement of the premises. But this was prohibited by
the second Law of this Figure, — that the Sumption must always
be universal. Let us try this rule in the foimula of Festino now
stated, reversing the premises.
Some S are M ; (i. e., some M.)
No P is M ;
( No P is some S.
{ J\o ir IS some a. )
I Some S are no P. j
Some actions are praiseworthy ;
No vice is 2:)7'aiservorthy ;
( No vice is some action. )
\ Some action is no vice. )
From what I have now said, it will be seen that the Dictum de
Omni et de Nullo cannot afford the principle of the Second Figure.
The same errors of the logicians, on which I have already com-
mented, in supposing that the sumption or major premise in this
figure must always be universal, — an error founded on another
error, that there is, (properly speaking), either sumption or sub-
sumption in this figure at all, — this error, I say, has prevented them
recognising a mood corresponding to Baroco, the first premise
being a particular negative, the second a universal affirmative, i. e.,
Baroco with its premises reversed. That this is competent is
SoO APPENDIX.
seen from the example of Baroco now given. Eeversing it we
have :
[Some d are not B ; Some aniinals are not {any) oviparous;
Alt di are B. All birds are {some) ovijyarous.
No a is somQ d; No bird is some animal;
Some d are no a.] Some animal is no bird.
(c) Author's Supreme Canons of Categorical Syllogisms.
[The supreme Canon or Canons of the Categorical Syllogism,
finally adopted by Sir W. Hamilton, are as follow :— ]
I. " For the Unfigured Syllogism, or that in which the terms
compared do not stand to each other in the reciprocal relation of
subject and predicate, being, in the same proposition, either both
subjects or (possibly) both predicates, — the canon is: — I)i so far
as two notions, (notions proper, or individuals), either both agree, or
one agreeing, the other does not, ivith a common third notion ; in
so far, these notions do or do not agree with each others
II. " For the Figured Syllogism, in which the terms compared
are severally subject and predicate, consequently, in reference to
each other, containing and contained in the counter wholes of In-
tension and Extension ; — the canon is : — What worse relation of
subject and predicate subsists between either of two terms and a
common thirds term, with ivhich one, at least, is positively re-
lated; that relation subsists between the tiuo terms themselves.
" Each Figure has its own Canon.
"First Figure ; — What worse relation of detei-mining, {predi-
cate), and of determined, (subject), is held by either of two
notions to a third, with which one at least is jjositively related ;
that relation do they immediately, (directly), hold to each other,
and indirectly, (mediately), its converse
"Second Figure ; — Wliat ivorse relation of determined, (sub-
ject), is held by either of two notions to a, third, tuith which one
at least is positively related ; that relation do they hold indif-
ferently to each other
" Third Figure; — What luorse relation of determining (predi-
cate), is held by either of two notions to a third, with which one
at least is positively related ; that relation do they hold indiffer-
ently to each other." "■
«■ Discussioiis, pp. 654, 055. — Ed.
APPENDIX. 351
{d) Ultra-total Quantification of Middle Term.
(1.) Lambert's Doctrine.
Lambert, Neues Organon.
Dianoiologie, § 193. "If it be indetermined how far A does,
or does not, coincide with B, but on the other hand we know that
A and B, severally, make up more than half, * the individuals
under C, in that case it is manifest, that a [linear] notation is
possible, and that of the two following kinds : —
C c,
B b,
A
" For since B and A are each greater than the half oi C, A is
consequently greater than C less by B ; and in this case, it is of
necessity that some A are B, and some B are A.^ We may
accordingly so delineate : —
C c,
A a,
B b,
seeing that it is indifferent, whether we commence with A or with
B. I may add, that the case which we have here considered does
not frequently occur, inasmuch as the comparative extension of
our several notions is a relation which remains wholly unknown.y
I, consequently, adduce this only as an example, that a legitimate
employment may certainly be made of these relations."
« It is enough if either A or B ex- counter to each other, with which Logic
ceed the halt' ; the other need be only is alwaj's conversant, (the Universal and
half. This, which Lambert here and Formal), — if the extension be not com-
hereafter overlooks, I have elsewhere plate, it is of no consequence to note its
had occasion to show. See below, p. 356. comparative amount. For Logic and
/3 In the original for A there is, by a Philosophy tend always to an unexclu-
typographical erratum, C. See PA. §208. sive generality; and a general conclu-
7 In reference to this statement, see sion is invalidated equally by a single
above, Z> /cm. § 179, and below, PA. § 157, adverse instance as by a thousand. It
where it is repeated and confirmed. Lain- is only in the concrete or real whole, —
bert might have added, that, as we rarely the whole quantitative or integrate, and,
can employ this relation of the compai-a- whether continuous or discrete, the
tive extension of our notions, it is still whole in which mathematics are exclu-
morerarely of any import that we should, sively conversant, but Logic and Philo-
For in the two abstract, or notional, sopby little interested, — that this rela-
wholes, — the two wholes correlative and tiou is of any avail or significance.
352 APPENDIX.
Phdnomenolugie, § v. Of the Prohahle —
" § 188. In so far as such propositions are particular, they may,
like all other particular propositions, be syllogistically employed ;
but no farther, unless we look to their degree of particularity, or
other proximate determination, some examples of which we have
adduced in the Dianoiologie, (§ 235 et seq.) Thus the degree of
ixarticularity may render a syllogism valid, which, without this,
would be incompetent. For example —
Three-fourths of A are B ;
Two-thirds of A are G ;
Therefore, some C are B.
The inference here follows, because three-fourths added to two-
thirds are greater than unity ; and, consequently, there must be,
at least, five-twelfths of A, wliich are at once B and C.
" § 204. In the Third Figure we have the middle term, subject
in both premises, and the conclusion, particular. If now, the
subjects of the two premises be furnished with fractions [i.e. the
middle term on both sides], both premises remain, indeed, parti-
cular, and the conclusion, consequently, indetermined. But, inas-
much as, in both premises, the degree of particularity is determined,
there are cases where the conclusion may be drawn not only with
probability, but with certainty. Such a case we have already
adduced, (§ 188). For, if both premises be affirmative, and the
sum of the fractions with which their subjects are furnished greater
than unity, in that case a ccmclusion may be drawn. In this sort
we infer with certainty : —
Threefourths of A are B ;
Two-thirds of A ai'e ;
Therefore, some C are B.
" § 205. If, however, the sum of the two fractions be less than
unity, as —
Onefourth of A are B ;
One-third of A are C,
in that case there is no certainty in any affirmative conclusion,
[indeed in any conclusion at all]. But if we state the premises
thus determinatelv, —
APPENDIX. 353
Three-fourths of A. are not B ;
Two-thirds of A. are not C ;
in that case, a negative conclusion may be drawn. For, from the
propositions, —
Threefourths of A are not B;
One-third of A are C ;
there follows — Some C are not B. And this, again, because the
sum of the two fractions, (three-fourths added to one-third), is
greater than unity." And so on ; see the remainder of this section
and those following, till § 211.
(2). Author's Doctrine.
Aristotle, followed by the logicians, did not introduce into his
doctrine of syllogism any quantification between the absolutely
universal and the merely particular predesignations, for valid rea-
sons. — 1°, Such quantifications were of no value or application in
the one whole, (the universal, potential, logical), or, as I would
amplify it, in the two correlative and counter wholes, (the logical,
and the formal, actual, metaphysical), with which Logic is con-
versant. For all that is out of classification, — all that has no refer-
ence to genus and .species, is out of Logic, indeed out of Philosophy ;
for Philosophy tends always to the universal and necessary. Thus
the hio;hest canons of deductive reasoning, the Dicta de Omni et
de Xullo, were founded on, and for, the procedure from the uni-
versal whole to the subject parts ; whilst, conversely, the principle
of inductive reasoning was established on, and for, the (real or pre-
sumed) collection of all the subject parts as constituting the uni-
versal whole. — 2°, The integrate or mathematical whole, on the
contrary, (whether continuous or discrete), tlie philosophers con-
temned. For whilst, as Aristotle observes, in mathematics genus
and species are of no account, it is, almost exclusively, in the
mathematical whole, that quantities are compared together, through
a middle term, in neither premise, equal to the whole. But this
reasoning, in which the middle term is never universal, and the
VOL. II. Z
354 APPENDIX.
conclusion always particular, is, — as vague, partial, and contingent,
— of little or no value in philosophy. It was accordingly ignored
in Logic ; and the predesignations mo7-e, most, &c., as I have said,
referred to universal, or (as was most common) to particular, or to
neither, quantity.'' This discrepancy among logicians long ago
attracted my attention ; and I saw, at once, that the possibility of
inference, considered absolutely, depended, exclusively on the quan-
tifications of the middle term, in both premises, being, together,
more than its possible totality — its distribution, in any one. At
the same time I was impressed — 1°, With the almost utter inutility
of such reasoning, in a philosophical relation ; and, 2°, Alarmed with
the load of valid moods which its recognition in Logic would in-
troduce. The mere quantification of the predicate, under the two
pure quantities of definite and indefinite, and the two qualities of
afiirmative and negative, gives (abstractly) in each figure, thirty-
six valid moods ; which, (if my present calculation be correct),
would be multiplied, by the introduction of the two hybrid or am-
biguous quantifications of a majority and a half, to the fearful
amount oi four hundred and eighty valid moods for each figure.
Though not, at the time, fully aware of the strength of these ob-
jections, they however prevented me from breaking down the old
limitation ; but as my supreme canon of Syllogism proceeds on the
mere formal possibility of reasoning, it of course comprehends all
the legitimate forms of quantification. It is ; — Wliat ivorst
relation of subject and j^^'edicate, subsists hetiveen either of two
terms and a common thii^d term, with which one, at least, is
positively related ; — that relation subsists between the two terms
themselves : in other words ; — In as far as two notions both agree,
or, one agreeing, the other disagrees, with a common third notion;
— in so far, those notions agree or disagree ivith each other. This
canon applies, and proximately, to all categorical syllogisms, — in
extension and comprehension, — affirmative and negative, — and of
any figure. It determines all the varieties of such syllogisms : is
developed into all their general, and supersedes all their special,
laws. In short, without violating this canon, no categorical rea-
soning can, formally, be wrong. Now this canon supposes, that
o [Cf. Corvinus, Instit. Phil. c. v. § Wallis, Instit. Log. L. ii. c. i, p. 100.
376, r- 123. lence, 1742. Reusch, 5th ed.— Ed.]
Wallis.] [Reusch, Syst. Log. § 360.
APPENDIX. 355
the two extremes are compared together through the saiiie com-
mon middle ; aud this cannot but be, if the middle, whether, sub-
ject or predicate, in both its quantifications together, exceed its
totality, though not taken in that totality in either premise.
But, as I have stated, I was moved to the reconsideriition of this
whole matter ; and it may have been Mr De Morgan's syllogism
in our correspondence, (p. 19), which gave the suggestion. The
result was the opinion, that these two quantifications should be
taken into account by Logic, as authentic forms, but then relegated,
as of little use in practice, and cumbering the science with a super-
fluous mass of moods."
Authoe's Doctrine — continued.
No syllogism can be formally wrong in which, (1°), Both jire-
mises are not negative ; and, (2°), The quantifications of the middle
term, whether as subject or predicate, taken together, exceed the
quantity of that term taken in its whole extent. In the former
case, the extremes are not compared together ; in the latter, they
are not necessarily compared through the same third. These two
simple rules, (and they both flow from the one supreme law), being
obeyed, no syllogism can be bad ; let its extremes stand in any
relation to each other as major and minor, or in any relation to
the middle tei^m. In other words, its premises may hold any
mutual subordination, and may be of any Figure.
On my doctrine, Figure being only an unessential circumstance,
and every proposition being only an equation of its terms, we
may discount Figm-e, &c., altogether ; and instead of the symbol
{ mm ) marking subject and predicate, we might use the alge-
braical sign of equality (=).
The rule of the logicians, that the middle term should be once at
least distributed, [or indistributable], {i. e., taken universally or sin-
gularly = definitely), is untrue. For it is sufficient if, in both the
premises together, its quantification be more than its quantity as a
whole, (Ultratotal). Therefore, a major part, (a more or mosi), in
one premise, and a half in the other, are sufficient to make it eSec-
tive. It is enough for a valid syllogism, that the two extreme notions
« Extract from A Letter to A. de p. 41. — Ed.
Moj-i/an, Esq., from Sir W. Haniillm,
356 APPENDIX.
should, (or should not), of necessity, partially coincide in the third,
or middle notion ; and this is necessarily shown to be the case, if
the one extreme coincide with the middle, to the extent of a half,
(Dimidiate Quantification) ; and the other, to the extent of aught
more than a half, (Ultradimidiate Quantification). The first
and highest quantification of the middle term ( : ) is sufiicient,
not only in combination with itself, but with any of all the three
inferior. The second ( . , ) suffices in combination with the high-
est, with itself, and with the third, but not with the lowest. The
third ( . ) suffices in combination with either of the higher, but not
with itself, far less with the lowest. The fourth and lowest ( , )
suffices only in combination with the highest. [1. Definite; 2.
Indefinito-definite ; 3. Semi-definite ; 4. Indefinite.]
(ist March 1847. — Very carefully authenticated.)
There are 4 quantities (, | . | ., | : ), affording (4 x 4), 16 pos-
sible double quantifications of the middle term of a syllogism.
Of these 10 are legitimate equivalents, (^: M : | : M. , | . , M ,
: M . I . M : I : M , I , M : 1 . , M. , I . , M . I . M . , ) ; and 6
illegitimate, as not, together, necessarily exceeding the quantity
of that term, taken once in its full extent ( . , INI , | , ^I • , | • M . |
.M, |,M. |,M,).
Each of these 16 quantified middle terms affords 64 possible
moods ; to wit, 16 affirmative, 48 negative ; legitimate and ille-
gitimate.
Altogether, these 16 middle terms thus give 256 affirmative and
768 negative moods ; which, added together, make up 1024 moods,
legitimate and illegitimate, for each figure. For all three figures
= 3072.
The ] legitimate quantifications of the middle terra afford, of
legitimate moods, 160 affirmative and 320 negative (=480) i.e.
each 16 affirmative and 32 negative moods, (=48) ; besides of
illegitimate moods, from double negation, 160, i.e., each 16. The
6 illegitimate quantifications afford, of affirmative moods, 96 ; of
APPENDIX. 357
simple negative moods, 192 ; of double negative moods, 96 (=
384). Adding all the illegitimates =544.
The 1024 moods, in each figure, thus afford, of legitimate, 480
moods, (1440 for all 3 Figs.) ; being of affirmative 160 (480 for 3
Figs.), of negative 320 (960 for 3 Figs.), of illegitimate 544 moods ;
there being excluded in each, from inadequate distribution alone,
(§), 288 moods, (viz. 96 affirmative 192 negative) ; from double
negation alone, (|), 160 moods ; from inadequate distribution and
double negation together, (§ j), 96 moods.
(.3). Mnemonic Verses.
A it affirms of this, tliese, all —
Whilst E deuies of any :
I, it affirms, whilst denies,
Of some (or few or many).
Thus A affirms, as E denies,
And definitely either :
Thus I affirms, as denies,
And definitely neither.
A half, left semi-definite,
Is worthy of its score ;
U, then, affirms, as Y denies,
This, neither less nor more.
Indefinite -definites,
To UI and YO we come ;
And that affirms, and this denies,
Of more, most, (half plus some.)
UI and YO may be called Indefinito-definite, either, (T), Because
they approximate to the whole or definite, [forming] more than its
moiety, or, (2°), Because they include a half, which, in a certain
sense, may be regarded as definite, and something, indefinite, over
and above.
358 APPENDIX.
VII.— INDUCTION AND EXAMPLE.
(See above, vol. i., p. 318.)
(a) Quotations feom Authors.
I. — Aristotle.
Aristotle, Prior Analytics, B. ii. c. 23. After stating that "we
believe all things either through [deductive] Syllogism or from In-
duction," he goes on to expound the nature of this latter process.
" Now, Induction, and the Syllogism from Induction, is the
inferring one extreme, [the major], of the middle through the
other ; if, for instance, B is the middle of A C, and, through C,
we show that A inheres in B. Thus do we institute Inductions.
In illustration : — Let A be long-lived, B, wanting-hile, and C,
individual long-lived animals, as man, horse, mule, &c. A, then,
inheres in the whole of C, (for all animal without hile is [at least
some] long-lived) ; but B, wanting hile, also [partially, at least]
inheres in all C.« If now C reciprocate with B, and do not go
beyond that middle, [if C and B, subject and predicate, are each
«- I have, however, doubts whether thus: — the individual animals wanting
the example which now stands in the bile are [all] long-lived ; consequently,
Organon, be that which Aristotle hira- [all] animals wanting bile are long-lived."
self proposed. It appears, at least, to F. 107, a. ed. Aid. Compare also the
have been considerably modified, pro- greatly later Leo Magentinus, on the
bably to bring it nearer to what was Prior Analytics, f. 41, a. ed. Aid. On
subsequently supposed to be the truth, the age of Magentinus, historians (as
This I infer as likely from the Commen- Saxius and Fabricius,) vary, from the
tary of Ammonius on the Prior Ana- seventh century to the fovirteenth. He
lytics, occasionally interpolated by, and was certainly subsequent to Michael
thus erroneously quoted under the Psellus, junior, whom he quotes, and,
name of a posterior critic, — Joannes, therefore, not before the end of the
surnamed Philoponus, &c. His woi-ds eleventh century ; whilst his ignorance
are, in reference to Aristotle, as follows : of the doctrine of Conversion, introduced
— " He wishes, through an example, to by Boethius, may show that he could
illustrate the Inductive process ; it is of hardly have been so recent as the four-
this intent. Let A be long-lived; B, teenth.
wanting hile; G, as crow, and the like. Aristotle, De Part. Animal, (L. iv. c.
Now he says: — that the crow and the stag, 2), says, "in some animals the gall
being animals without bile and long- [bladder] is absolutely wanting, as in the
lived ; therefore, animal wanting bile is horse, mule, ass, stag, and roe.". . . "It
long-lived. Thus, tlu-ough the last [or is, therefore, evident that the gall serves
minor], do we connect the middle term no useful purpose, but is a mere excre-
with the [major] extreme. For I argue tion. Wherefore those of the ancients say
APPENDIX.
359
all tlie other], it is of necessity that A, [some, at least], should
inhere in [all] B, Por it has been previously shown,« that if any
two [notions] inhere in the same [remote notion], and if the
middle ^ reciprocate with either [or with both] ; then will the
other of the predicates [the syllogism being in the third figure]
inhere in the co-reciprocating extreme. But it behoves us to con-
ceive C as a complement of the wliole individuals ; for Induction
has its inference through [as it is of] all. 7
■«'ell, who declare that the cause of lon-
gevity is the abseuce of the gall ; and this
from their observation of the solidun-
gula and deer, for animals of these
classes want the gall, and are long-lived."
Hist. An., L. ii. c. 11, Schn. 18, Seal. 15
vul. Notices that some animals have,
others want, the gall bladder, {xo>^h, v.
Schn. iii. p. 1 06), at the liver. Of the latter,
among viviparous quadrupeds, he notices
stag, roe, horse, mule, ass, &c. Of birds
who have the gall-bladder apart from
the liver and attached to the intestines,
he notices the pigeon, crow, &c.
* Aristotle refers to the chapter im-
mediately preceding, which treats of the
Reciprocation of Terms, and in that to
the fifth rule which he gives, and of the
following purport. " Again, when A and
B inhere in all C [/.e. all C is A and is B],
and when reciprocates [i.e. is of the
same extension and comprehension] with
B, it is necessary that A should inhere in
all B [i.e. that all B should be A] ."
)3 For oLKpov, I read /JLeaov ; but per-
haps the true lection is — irphs tovto
Barepov uvrSiiv avTi(rTpe<prj twv &Kpoov.
The necessity of an emendation becomes
manifest from the slightest consideration
of the context. In fact, the common
reading yields only nonsense ; and this
on sundry grounds. — 1°, There are three
things to which Odrepov is here appli-
cable, and yet it can only apply to two.
But if limited, as limited it must be,
to the two inhei-ents, two absurdities
emerge. 2°, For the middle, or common,
notion, in which both the others inhere,
that, in fact, here exclusively wanted, is
alone excluded. 3°, One, too, of the in-
herents is made to reciprocate with either ;
that is, with itself, or other. 4°, Of the
two inherents, the minor extreme is that
which, on Aristotle's doctrine of Induc-
tion, is alone considered as reciprocating
with the middle or common term. But,
in Aristotle's language, rh &Kpov, " The
Extrem.e, " is (like t} irp6Ta<ris, The Pre-
position in the common language of the
logicians) a synonyme for the major, in
opposition to, and in exclusion of, the
minor, term. In the two short corre-
lative chapters, the present and that
which immediately follows, on Induc-
tion and on Example, the expression, be-
sides the instance in question, occurs at
least seven times; and in all as the major
term, — 5°, The emendation is required
by the demonstration itself, to which
Aristotle refers. It is foiind in the
chapter immediately preceding (§ 5) ;
and is as follows : — " Again, when A and
B inhere in all C ; and when C recipro-
cates with B ; it necessarily follows that
A should [partially, at least], inhere in
all B. For whilst A [some, at least], in-
heres in all C ; and [all] C, by reason of
their reciprocity, inheres in [all] B ; A
will also [some, at least], inhere in all
B." The mood here given is viii. of our
Table. (See below. Appendix XI.)
7 This requisite of Logical Induction,
— that it should be thought as the re-
sult of an agreement of all the indivi-
duals or parts, — is further shown by
Aristotle in the chapter immediately
following, in which he treats the reason-
ing from Example. See passage quoted
on this page (§ 5).
360 APPENDIX.
" Tins kind of syllogism is of the primary and immediate pro-
position. For the reasoning of things mediate is, through their
medium, of things immediate, through Induction. And in a cer-
tain sort, Induction is opposed to the [Deductive] Syllogism. For
the latter, through the middle term, proves the [major] extreme
of the third [or minor] ; whereas the former, through the third, [or
minor term, proves] the [major] extreme of the middle. Thus,
[absolutely], in nature, the syllogism, through a medium, is the
prior and more notorious ; but [relatively] to us, that through In-
duction is the clearer."
An. Pr., L. ii. c. 24. Of Example. — § 1. "Example emerges,
when it is shown that the [major] extreme inheres in the middle,
by something similar to the third [or minor term] ... § 4.
Thus it is manifest that the Example does not hold the relation
.either of a whole to part [Deduction], nor of a part to whole
[Induction], but of part to part ; when both are contained under
the same, and one is more manifest than the other. § 5. And
[Example] differs from Induction, in that this, from all the indi-
viduals, shows that the [major] extreme inheres in the middle, and
does not [like Deduction] hang the syllogism on the major ex-
treme ; whereas that both hangs the syllogism [on the major ex-
treme], and does not show from all the individuals [that the major
extreme is inherent in the minor.]"
An. Post., L. i. c. 1, § 8. — " The same holds true in the case of
Teasonings, whether through [Deductive] Syllogisms or through
Induction ; for both accomplish the instruction they afford from
information foreknown, the former receiving it as it were from the
tradition of the intelligent, the latter manifesting the universal
through the light of the individual." (Pacii, p. 413. See the rest of
the chapter).
An. Pus., L. i. c. 18, § 1. — "But it is manifest that, if
any sense be wanting, some relative science should be wanting
likewise, this it being now impossible for us to apprehend. For
we learn everything either by induction or by demonstration.
Now, demonstration is from universals, and induction from parti-
culars ; but it is impossible to speculate the universal unless
through induction, seeing that even the products of abstraction
will become known to us by induction."
APPENDIX.
361
A. Aristotle's Errors regardiiio- Induction.
Not making Syllogism and its theory superior and common to
both Deductive and Inductive reasonings,
A corollary of the preceding is the reduction of the genus Syllo-
gism to its species Deductive Syllogism, and the consequent con-
tortion of Induction to Deduction.
B. Omissions.
Omission of negatives.
Of both terms reciprocating.
C. Ambiguities.
Confusion of Individuals and Particular. See Scheibler, [Ojjera
Logica, P. iii. De Pro})., c. vi., tit. 3, 5. — Ed.]
Confasion or non-distinction of Major or Minor extremes.
The subsequent observations are intended only to show out
Aristotle's authentic opinion, which I hold to be substantially the
true doctrine of Induction ; to expose the multiform errors of his
expositors, and their tenth and ten times tenth repeaters, would be
at once a tedious, superfluous, and invidious labour. I shall, first
of all, give articulately the correlative syllogisms of Induction and
Deduction which Aristotle had in his eye ; and shall employ the
example which now stands in the Organon, for, though physio-
logically false, it is, nevertheless, (as a supposition), valid, in illus-
tration of the logical process.
AEISTOTLES COEEELATIVE SYLLOGISMS.
{a) Of Induction.
All C {man, liorse, mule, &c.) is
some A {lonfj-lived) ;
All G {man, horse, mule, &c.) is
alt B {ivantiny-hile) ;
AW^ {luanting-hile) is some A
{long-lived).
(6) Of Deduction.
All^ {wanting-hile) is some A
{long-lived) ;
AUG {inan, horse, mule, &c.) is
all B {wanting-hile) ;
All G {man, horse, mule, &c.) is
some A {long-lived).
A,
C(p,q,r,&c.): — :B A,
B:
; C (p, q, r, &c.)
362 APPENDIX.
These syllogisms, tliongli of different figures, fall in the same
mood ; in our table they are of the eighth mood of the third and
first Figures. Both imallowed. (See Ramus, quoted below, p. 363).
The Inductive syllogism in the first figure given by Schegkius,
Pacius, the Jesuits of Coimbra, and a host of subsequent repeaters,
is altogether incompetent, so far as meant for Aristotle's correla-
tive to his Inductive syllogism in the third. Neither directly nor
indirectly does the philosopher refer to any Inductive reasoning
in any other figure than the third. And he is right ; for the third
is the figure in which all the inferences of Induction naturally
run. To reduce such reasonino;s to the first figure, far more to the
second, is felt as a contortion, as will be found from the two fol-
lowing instances, the one of which is Aristotle's example of In-
duction, reduced by Pacius to the first figure, and the other the
same example reduced by me to the second. I have taken care
also to state articulately what are distinctly thought, — the quanti-
fications of the predicate in this reasoning, ignored by Pacius and
logicians in general, and admitted only on compulsion, among
others, by Derodon, (below, p. 363), and the Coimbra commen-
tator."
Aristotle's inductive syllogism in piciuees.
(c). Fig. I. (J). Fig. II.
All G {man, horse, mule, <fec.) is Some A {long-lived) is all G
some A {long-lived) ; {jnan, horse, mule, &c.) ;
All ^ (wanting -bile) is all G All H {ivanting-hile) is all G
{man, horse, mule, &c.) / {man, horse, mule, &c.) ;
All B {luanling-hile) is some A All B {wanting-hile) is some A
{long-lived). {long-lived).
II. — Pachymeres.
Pachymercs, Epitome of Aristotle s Logic, (Title viii. cli. 3,
c. 1280). — " Induction, too, is celebrated as another instrument
of philosophy. It is more persuasive than Deductive reasoning ;
for it proposes to infer the universal from singulars, and, if
possible, from all. But as this is frequently impossible, indivi-
o [In An. Prior., L. ii. p. 403. Cf. (1544). Tosca, Conip. Phil. Logica, t.
Perionius, Dialect ira, L. iii. p. 356 I. 1. iii. c. 1, p. 115.]
APPENDIX. 363
duals being often in number infinite, there has been found a
method through which we may accomplish an Induction, from
the observation even of a few. For, after enumerating as many
as we can, we are entitled to call on our adversary to state on
his part, and to prove, any opposing instances. Should he do
this, then [for, ' data instantia, cadit inductio'] he prevails ; but
should he not, then do we succeed in our Induction. But Induction
is brought to bear in the third figure ; for in this figure is it origi-
nally cast. Should, then, the minor premise be converted, so that
the middle be now predicated of all the minor extremes, as that
extreme was predicated of all the middle ; in that case, the con-
clusion will be, not of some, but of all. [In induction] the first
figure, therefore, arises from conversion, — from conversion of the
minor premise, — and this, too, converted into all, and not into
so)ne. But [an inductive syllogism] is drawn in the third figure,
as follows : — Let it be supposed that we wish to prove, — every
animal moves the lower jaiu. With that intent, we place as
terms : — the major, moves the under jaw ; the minor, \all\ ani-
mal ; and, lastly, the middle, all contained under animal, so that
these contents reciprocate with all animal. And it is thus perfected
[?] in the first figure, as follows : — To move the lower jaw is predi-
cated of all individual animals ; these all are predicated of all
animcd; therefore, moving the lower jccw is predicated of all ani-
mal. In such sort induction is accomplished."
III. — Eamus.
Ramus, Schoke Dialecticce, L. viii. c. 11. "Quid vero sit in-
ductio perobscure [Aristoteli] declaratur: nee ab interpretibusintel-
ligitur, quo modo syllogismus per medium concludat majus extre-
mum de minore: inductio majus de medio per minus." Ramus has
confirmed his doctrine by his example. For, in his expositions, he
himself is not correct.
IV. — Deeodon.
Derodon, Logica Bestituta, 1659, p. 602. Philosophia Con-
tracta, 1661', Logica, p. 91. "Induction is the argumentation in
which, from all the particulars, their universal is inferred ; as —
Fire, air, water, earth, are bodies ; therefore, every element
364 APPENDIX.
is hody. It is recalled, however, to syllogism, by assuming all
the particulars [including singulars] for the middle term, in this
manner : — Fire, air, water, and ea7'th are bodies ; hut fire, air,
water, and earth are every element ; therefore, every element is
hody. Again : — The head, chest, feet, cfcc, are diseased ; hut
the head, chest, feet, <&c., are the whole animal ; therefore, the
ivhole animal is diseased. Thus Induction is accomplished, when,
by the enmneration of all the individuals, we conclude of the
species what holds of all its individuals ; as — Peter, Paul, James,
&c., are rational; thej^efore, all man is rational; orwhen, by the
enumeration of all the sj)ecies, we conclude of the genus what holds
of all its species; as — Man, ass, horse, d'C, are sensitive; there-
fore, all animal is sensitive ; or when, by the enumeration of all
the parts, we conclude the same of the whole ; as — Head, chest,
feet, &c., are diseased ; therefore, the whole animal is diseased."
v.— The College of Alcala.
A curious error in regard to the contrast of the Inductive and
the Deductive syllogism stands in the celebrated Cursus Complu-
tensis, — in the Disputations on Aristotle's Dialectic, by the Car-
melite College of Alcala, 1624, (L. iii. c. 2). We there find sur-
rendered Aristotle's distinctions as accidental. Induction and
Deduction are recognised, each as both ascending and descending,
as both from, and to, the whole ; the essential difference between
the processes being taken, in the existence of a middle term for
Deduction, in its non-existence for Induction. The following is
given as an example of the descending syllogism of Induction : —
All men are animals; therefore, this, and this, and this, etc., man
is an animal. An ascending Inductive syllogism is obtained from
the i^receding, if reversed. Now all this is a mistake. The syllo-
gism here stated is Deductive ; the middle, minor, and major
terms, the minor premise and the conclusion being confounded
together. Expressed as it ought to be, the syllogism is as follows : —
All men are {some) animals ; this, and this, and this, cC'c, are
(constitute) all men; thei-efore, this, and this, and this, d:c., are
{some) animal. Here the middle term and three propositions re-
appear ; whilst the Deductive syllogism in the first figure yields, of
course, on its reversal, an Inductive syllogism in the third.
APPENDIX. 365
The vulgar errors, those till latterly, at least, prevalent in this
country, — that Induction is a syllogism in the Mood Barbara of
the first figure, (with the minor or the major premise usually sup-
pressed) ; and still more that from a some in the antecedent, we
can logically induce an all in the conclusion ; — these, on their own
account, are errors now hardly deserving of notice, and have been
already sufficiently exposed by me, upon another occasion, (Edin-
burgh Review, LVII. p. 224 et seq.) [Discussions, p. 158 et seq.
—Ed.]
VI. — Facciolati.
Facciolati, Rudimenta Logica, P. iii. c. 3, defines Induction
as " a reasoning without a middle, and concluding the universal
by an enumeration of the singulars of which it is made up." His
examples show that he took it for an Enthymeme. — " Prudence,
Temperance, Fortitude, &c., are good habits, [tJiese constitute all
virtue] ; therefore, [(dl] virtue is a habit."
VII. — Lambert.
Lambert, Neues Organon, i. § 287. "When, in consequence of
finding a certain attribute in all things or cases which pertain to a
class or species [genus (?)], we are led to affirm this attribute of
the notion of the class or genus ; we are said to find the attribute
of a class or genus through induction. There is no doubt that
this succeeds, so soon as the induction is complete, or so soon as we
have ascertamed that the class or species A contains under it no
other cases than C, D, E, F, M, and that the attribute B occurs
in each of the cases C, D, E, F, M. This process now pre-
sents a formal syllogism in Caspida. For we thus reason — •
C, as well as T>, E, F, M are allB;
But A is either C, or D, or E, or F or M ;
Consequently, all A are B.
"The example previously given of the syllogistic mood Gas-
pida, may here serve for illustration. For, to find whether every
syllogism of the Second Figure be negative, we go through its seve-
ral moods. These are Cesare, Gamestres, Festino, Baroco. Now
36C APPENDIX.
both the first conclude in E, both the last in O. But E and are
negative, consequently all the four, and herewith the Second Figure
in general, conclude negatively.a As, in most cases, it is very diffi-
cult to render the minor proposition, which has the disjunctive
predicate for its middle term, complete, there are, therefore, com-
petent very few perfect inductions. The imperfect are [logically]
worthless, since it is not in every case allowable to argue from
so7ne to all. And even the perfect we eschew, whensoever the
conclusion can be deduced immediately from the notion of the
genus, for this inference is a shorter and more beautiful."
Strictures on Lambert's doctrine of Induction.
1°, In making the minor proposition disjunctive.
2°, In making it particular.
3°, In making it a minor of the First Figure instead of the
Third.
Better a categorical syllogism of the Third Figure, like Aris-
totle, whom he does not seem to have been aware of. Eefuted by
his own doctrine in § 230.
The recent German Logicians,(3 following Lambert, {N. Org.
i. § 287), make the inductive syllogism a byeword. Lambert's
example: — "C, as well as D, E, F M, all are B; but A
is either C, ur D, or E, or F, or M ; thei^efore, all A is B."
Or, to adapt it to Aristotle's example : — Man, as well as horse,
mule, &c., all are long-lived animals ; hut animal void of gall is
either man, or horse, or mule, &c. ; therefore, all animal void of
gall is long-lived.
This, I find, was an old opinion ; and is well invalidated by the
commentators of Louvain.7
a. It is given in § 285, as follows :— that the singulars in the Inductive syllo-
" The syllogisms, as tvell in Cesare as in gism should be enumerated by a disjuuc-
Camestres, Festino, and Baroco, are all tive conjunction, in so much that the
negative; premises of such a syllogism are com-
'' Now every syllogism of the Second monly wont to be thus cast: — What-
Figiore is either in Cesare, or Camestres, soever is John, or Peter, or Paid, dx., is
or Festino, or Baroco; cajmhle of instruction. But they err,
"Consequently every syllogism in the not observing that the previous proposi-
Second Figure is negative." tion is manifestly equivalent to the fol-
/3 As Herbart, Lehrhuch der Logik, § lowing, — John, and Peter, and Paid,
69. Twesten, Drobisch, II. Ritter. dr., are capable of instruction" (Lo-
7 " I am aware of the opinion of many, vnnienses. Com. In An. Pr., L. ii. tr.
APPENDIX. 367
The only inducement to the disjunctive form is, that the predicate
is exhausted without the predesignation of universality, and the
'First Figure attained. But as these crotchets have been here
refuted, therefore, the more natural, &c.
Some logicians, as Oxford Crakanthorpe, {Logica, 1. iii., c. 20,
published 1622, but written long before), hold that Induction can
only be recalled to a Hypothetical syllogism. As, — If Sophocles
he risible, likewise Plato and all other men, then all man is insihle;
hut Socrates is risible, likewise Plato and all other men; thei-efore,
all man is risible. Against the Categorical syllogism in one or
other figure he argues : — "This is not a universal categorical, because
both the premises are singular ; nor a singular categorical, because
the conclusion is universal." It is sufficient to say, that, though
the subjects of the premises be singular, (Crakanthorpe does
not contemplate their being particular), as supposed to be all the
constituents of a species or relatively universal whole, they are
equivalent to that species ; their universality, (though contrary to
Aristotle's canon), is, indeed, overtly declared, in one of the pre-
mises, by the universal predesignation of the iwedicate. Our
author further adds, that Induction cannot be a categorical syl-
logism, because it contains four terms ; this quaternity being
3, c. 2, p. 286, ed. 1547 ; 1st ed., All that is Socrates, or Plato, {and so
1555). This here said of the major of others), runs ; hut all man is Socrates,
is true of Lambert's minor. The Lou- or Plato, {and so of others) ; therefore, all
vain masters refer probably [to Ver- 'nmn runs. And these singulars ought
sor, &c.] This doctrine, — that the to be taken disjunctively, and disjunc-
Inductive syllogism should be drawn tively, not computatively, verified of
in a disjunctive form, — was commonly their universal " — {In. Hisp. Summul,
held, esijecially by the scholastic com- Tr. v.)
mentators on Petrus Hispauus. Thus The same doctrine is held in the Re-
Versor, (to take the books at hand), ■parationes of Arnoldus de Tuugeri and
whose £'.iyws/<«o?i first appeared in 1487, the Masters Regent in the Burse (or
says — " In the fourth place. Induction College) of St Lawrence, in Cologne,
is thus reduced to syllogism, seeing that, 1496. (Tr. iii., c. ii., Sec. Pri.)
in the conclusion of the Induction, there It is also maintained in the Copulata
are two terms of which the subject forms of Lambertus de Monte, and the other
the minor, and the predicate the major. Regents in the Bui-sa Montis of Cologne,
extreme in the syllogism ; whilst the 1490. They give their reasons, which
singulars, which have no place in the are, however, not worth stating and re-
conclusion, constitute the middle term, futiug.
Thus the Induction — Socrates runs. But Tartaretus, neither in his Com-
Plato runs, {and so of other men) ; there- mentaries on Hispanus nor on Aris-
fore, all man runs,—\s, thus reduced : totle, mentions this doctrine.
368 APPENDIX.
made by the " all men," (in his example), of the premises being
considered as different from the "all man" of the conclusion.
This is the veriest trifling. The difference is wholly factitious :
all man, all men, &c., are virtually the same ; and we may in-
differently use either or both, in premises and conclusion.
(h) Mateeial Induction.
Material or Philosophical Induction is not so simple as com-
monly stated, but consists of two syllogisms, and two deductive
syllogisms, and one an Epicheirema. Thus : —
I. — What is found true of some constituents of a natural class,
is to he 'presumed true of the tvhole class, {for nature is always
uniform) ; a a a' are some constituents of the class A ; therefore,
ivhat is true of a a a" is to he presumed true of A.
II. — What is true of a a a" is to he presumed true of A;
hut z is time of a a' a" ; therefore, z is true <f A.
It will be observed, that aU that is here inferred is only a pre-
sumjotion, founded, 1°, On the supposed uniformity of nature ;
2°, That A is a natural class ; 3°, On the truth of the observation
that a a a" are really constituents of that class A ; and, 4°, That
z is an essential quality, and not an accidental. If any be false,
the reasoning is naught, and, in regard to the second, a a' a," (some)^
cannot represent A, (all), if in any instance it is found untrue.
"Data instantia cadit inductio." In that case the syllogism has
an undistributed middle.
APPENDIX.
309
VIII.
HYPOTHETICAL AND DISJUNCTIVE EEASONING—
IMMEDIATE INFERENCE.
A.— AUTHOR'S DOCTRINE— FRAGMENTS.
(See above, Vol. I. p. 326.)
All Mediate inference is one ; that
cal ; for the Conjunctive and Disjun
reasoning are reducible to immediate
incorrectly called Categori-
ctive forms of Hypothetical
inferences.
Immediate ;
of which some
kinds are
Recognised,
as Prepositional.
(Various.)
Not recognised,
as Syllogistic,
Mediate ;
Syllogism Proper,
(Categorical.)
A) Analytic.
B) Synthetic.
Disjunctive,
Conjunctive,
a) Unfigured.
\ b) Figured,
(Intensive
or Exten-
sive) in
Hypo-
thetical.
F. I.
F. II.
F. III.
to M
§ 1. Reasoning is the showing out explicitly that a proposition,
not granted or supposed, is implicitly contained in something
different, which is granted or supposed.
§ 2. What is granted or supposed is either a single proposition,
or more tlian a single proposition. The Reasoning, in the former
case, is Immediate, in the latter, Mediate.
§ 3. The proposition implicitly contained, may be stated first
or last. The Reasoning, in the former case, is Analytic, in the
latter, Synthetic.
Observations. — § 1. "A proposition," not a truth ; for the pro-
position may not, absolutely considered, be true, but relatively
to what is supposed its evolution, is and must be necessary,
All Reasoning is thus hypothetical ; hj^pothetically true,
a Reprinted from Discussions, p. 65G. — Ed.
VOI,. II.
2 A
870 APPENDIX.
though absolutely what contains, and, consequently, what is
contained, may be false."
Observations. — § 2. Examples : Immediate — If A is B, then
a is A; Mediate — If A is B, cmd B is C, then A is C.
Observations. — § 3. Examples : Analytic — B is A, for A ts B ;
A is C, for A is B, and B is C. Synthetic — A is B ; there-
fore, B is A ; A is B, and B is C ; therefore, A is C.
On the Nature and Divisions of Inference or Syllogism
in general.
(November 1848.)
I. Inference, what
II. Inference is of three kinds ; what I would call the — 1°, Com-
mutative ; 2°, Explicative ; and, 3°, Comparative.
1°, In the first, one proposition is given ; and required what are
its formal commutations ?
2°, In the second, two or more connected propositions are given,
under certain conditions, (therefore, all its species are conditionals) ;
and required what are the formal results into which they may be
explicated. Of this genus there are two species, — the one the Dis-
junctive Conditional, the other the Conjunctive Conditional. In
the Disjunctive, (the Disjunctive also of the Logicians), two or
more proj^ositions, with identical subjects or predicates, are given,
under the disjunctive condition of a counter quality, i. e. that
one only shall be affirmative ; and it is required what is the
result in case of one or other being affirmed, or one or more denied.
(Excluded Middle.) In the Conjunctive, (the Hypotheticals of
the logicians), two or more propositions, convertible or contradic-
tory, with undetermined quality, are given, under the conjunctive
condition of a correlative quality, i. e. that the affirmation or
a. That all logical reasoning is hypo- consequentice and iiccessitas consequent-is,
thetical, and that Categorical Syllogism see Scotus, Qua'stiones, Super Elenchos,
is really, and in a higher signification, qu. iv., p. 227, ed. 1639, and that all
hypothetical, see Maimon, Versuch einer inference hypothetical, In An. Prior.,
ncuen Logik, § vi. l.jp-p. 82,88. E. Rein- L. ii. qu. i. p. 331. Apuleius, Z>e i7a6.
hold, Loffik, § 109, p. 253 et seq. Smig- Doct. Plat., p. 34. Aristotle, .4 w. Prior,
lecius, Zor//ca, Disp. xiii., q. 5, p. 495, (1st i. 32, § 5. Smiglecius, Logica, loc. cit.
ed. 1616). Balforeus, In Arist. Org., An. Prior., i.,
On the nature of the Necessity in Syl- t. 8, p. 454, 1616. [See also Discussions,
logisticlnference; distinction of Formal p. 146, note.— Ed.]
and Material Necessity, or of necessitas
APPENDIX. 371
negation of one being determined, determines the corresponding
affirmation or negation of the other or others ; and it is required
what is the result in the various possible cases. (Identity and
Contradiction, not Sufficient Keason, which in Logic is null as a
separate law).
8°, In the third, three terms are given, two or one of which are
positively related to the third, and required what are the relations
of these two terms to each other? ""
III. All inference is hypothetical.
IV. It has been a matter of dispute among logicians whether
the class which I call Explicative, (viz. the Hypothetical and Dis-
junctive Syllogisms), be of Mediate or Immediate inference. The
immense majority hold them to be mediate ; a small minority, of
which I recollect only the names of Kant, [Fischer, Weiss, Bouter-
wek, Herbart],^ hold them to be immediate.
The dispute is solved by a distinction. Categorical Inference is
mediate, the medium of conclusion being a term ; the Hy])othetical
and Disjunctive syllogisms are mediate, the medium of conclusion
being a proposition, — that which I call the Explication. So far
they both agree in being mediate, but they differ in four points.
The first, that the medium of the Comparative syllogism is a term ;
of the Explicative a proposition. The second, that the medium of
the Comparative is one ; of the Explicative more than one. The
third, that in the Comparative the medium is always the same; in
the Explicative, it varies according to the various conclusion. The
fourth, that in the Comparative the medium never enters the con-
clusion ; whereas, in the Explicative, the same proposition is reci-
procally medium or conclusion.
V. Logicians, in general, have held the Explicative class to be
composite syllogisms, as compared with the Categoric ; whilst a
« A better statement of the three dif- third; — what are the inferences afforded
f erent processes of Reasoning. in the relations to each other, which this
I. Given a proposition ; commutative ; comparison of the two notions to the
— what are the infei'ences which its com- third determines?
mutations afford ? [;8 Kant, Logik, § 75. Bouterwek,
II. Given two or more propositions ; Lehrhuch der philosopMscJien Vorlcennt-
related and conditionally; — what are «/s6r, § 100, p. 158, 2d ed. 1820. Fischer,
the inferences which the relative pro- Loyik, c. v. §§ 99, 100, p. 137. Weiss,
positions, explicated under these con- Logik, §§ 210, 251. Herbart, Lehrhuch
ditions, afford ? zur Eiiileituny in die Philosoj;)hie, § 64,
III. Given three notions ; two re- p. 87, 1834.]
lated, and at least one positively, to a
372 APPENDIX.
few have held them to be more simple. This dispute arises from
each party taking a partial or one-sided view of the two classes.
In one point of view, the Explicative are the more complex, the
Comparative the more simple. In another point of view, the
reverse holds good.
Our Hypothetical and Disjunctive Syllogisms may be reduced
to the class of Exj^licative or Conditional. The Hypotheticals
should be called, as they were by Boethius and others. Con-
junctive, in contrast to the co-ordinate species of Disjunctive.
Hypothetical, as a name of the species, ought to be abandoned.
The Conjunctives are conditional, inasmuch as negation or affir-
mation is not absolutely asserted, but left alternative, and the quality
of one proposition is made dependent on another. They are, how-
ever, not jjroperly stated. The first proposition, — that contain-
ing the condition, — which I would call the Explicand, should be
thus enounced : J.s B, so A ; — or, As^ is, so is A ; or. As C is
B, so is B A. Then follows the proposition containing the expli-
cation, which I would call the Explicative ; and, finally, the
proposition embodying the result, which I would call the Ex-
ptlicate.
They are called Conjunctives from their conjoining two con-
vertible propositions in a mutual dependence, of which either may
be made antecedent or consequent of the other.
Disjunctive Syllogisms are conditional, inasmuch as a notion is
not absolutely asserted as subject or predicate of another or others,
but alternatively conjoined with some part, but only with some
part, of a given plurality of notions, the affirmation of it with one
part involving its negation with the others. The first proposition,
containing the condition, I would call the Explicand, and so forth
as in the Conjunctives. They are properly called Disjunctives.
DlSTPJBUTION OP EeASONINGS.
(Nov. 1848.) — Inference maybe thus distributed, and more fully
and accurately than I have seen. It is either, (I.) Immediate, that
is, without a middle term or medium of comj)arison ; or (II.) Me-
diate, with such a medium.a
a [Cf. Fonseca, Instit. Dial., L. vi. PMlosophice Quadripartita, Dialecflra,
c. 1., 1st ed. 15G4. Eustachius, ,?(«««(* P. iii. tract, i., p. 112. [" Quoniam
APPENDIX. 373
Both the Immediate and the Mediate are subdivided, inasmuch
as the reasoning is determined (A) to one, or (B) to one or other,
conclusion. (It is manifest that this latter division may constitute
the principal, and that immediate and mediate may constitute
subaltern classes.)
All inference, I may observe in the outset, is hypothetic, and
what have been called Hypothetical Syllogisms are not more hypo-
thetic than others.
I. A — Immediate Peremptory Inference, determined one con-
clusion, contains under it the following species : — a
I. B — Immediate Alternative Inference contains under it these
five species, —
1°, Given one proposition, the alternative of aflSrmation and nega-
tion. As — A either is or is not ; hut A is ; therefore A is not not.
Or, A is or is not B ; but A is B ; therefore, A is not not-B.
This species is anonymous, having been ignored by the logi-
cians; but it requires to be taken into account to explain the
various steps of the process.
2°, Given one proposition, the alternative between different pre-
dicates. This is the common Disjunctive Syllogism.
argumentatio est quasdam consequentia, secutione, p. 492 et seq.'\
(latius enim patet consequentia quam o [Kinds of Immediate Inference. —
ai-gumentatio), prius de consequentia, I. Subalternation. II. Conversion. III.
quam de argumentatione dicendum est. Opposition — (a) of Contradiction — (b)of
Consequentia igitur, sive consecutio, est Contrariety — (c) of Subcontrariety. IV.
oratio in qua ex aliqiio aliquid colligitur ; Equipollence. V. Modality. VI. Con-
ut, Omnis homo est animal, igitur aliquis traposition. VII. Correlation. VIII.
homo est animal."- — Ed.] [Whether Im- Identity.
mediate Inference really immediate, see, Fonseca (IV), (I), (II). Eustachius (I),
on the affirmative, E. Reinhold, Logil; (IV), (II), (VIII). Wolf, (IV), (VII),
§106; on the negative, Wolf, P/t(7.i?rt<., (Ill), a, b, c, (II). Stattler, (I), (IV),
§ 461. Krug, Lof/lh, § 94, p. 287. (ID, (III). Kant, (I), (III), a, b, c), (II),
Schulze, Logik, §§ 85-90, (§ 80, 5th ed.). (VI). E. Reinhold, (I), (II), (VI), (VII).
Cf. Maimon, Versuch einer neuen Logil; Rosling, (I), (IV), (II), (III), a, b, c, (V),
Sect. V. § 2, p. 74 et seq. F. Fischer, Krug, (IV), (I), (III), a, b, c, (II), (V).
Logik, p. 104 et seq. Bachmann, Logik, G. E. Schulze, (IV), (I), (III), (II). S.
§ 105, p. 154 et seq. Reimarus, Ver- Maimon, (I), (III), (II), (VI). Bachmann,
7iimftlehre,%159 et seq. (1765). Bolzano, (IV), (I), (III), a, b, c, (II), (VI), (V).
Wissenschaftslehre, Logik, vol. ii. § 255 Platner, (I), (II), (III), (IV). F. Fis-
et seq. Twesten, Logik, inshesondere die cher, (V), (I), (III), (II), (VI). Reimarus,
Analytik, § 77, p. 66. Rosling, Die IV., (I), (III), a, b, (II . Twesten, I),
Lehren der reinen Logil; § 130, p. 391. (V), (III), (IV), (II), (VI). See above
Scheibler, 0/3. Log., De Proposit. Con- pp. 283, 284.]
374 APPENDIX.
3°, The previous ji repositions conjoined, given one proposition,
&c. As, A either is or is not either B or C or D; hut A is B ;
therefore it is not not B, it is not C, it is not D.
Alias, A is either B or non-'B, or C or non-G, or D or 7ion-D ;
hut A isB; therefore it is not non-B, and it is non-C, and it is
non-D.
4", Given two propositions, second dependent on the first, and in
the first the alternative of affirmation and negation. This is the
Hypothetical Syllogism of the logicians. It is, however, no more
hypothetical than any other form of reasoning ; the so-called
hypothetical conjunction of the two radical propositions being
only an elliptical form of stating the alternation in the one, and
the dependence on that alternation in the other. For example, —
If A is B, B is G ; this merely states that A either is or is not B,
and that B is or is not C, according as A is or is not B. In
short — As A is or is not B, so B is or is not 0.
(Errors, — 1°, This is not a mediate inference.
2°, This is not more composite than the categorical.
3°, The second f)roposition is not more dependent upon the first,
than the first upon the second.)
5", Given two propositions, one alternative of affirmation and
negation, and another of various predicates ; the Hypothetico-
disjunctive or Dilemmatic Syllogism of the logicians.
II. A — Mediate Peremptory Inference. This is the common
Categorical Syllogism. Three propositions, three actual terms,
one primary conclusion, or two convertible equally and conjunctly
valid.
II. B — Mediate Alternative Syllogism. Three propositions,
three possible terms, and conclusions varying according ....
2°, The Disjunctive Categorical.
4°, The Hypothetical Categorical.
5", Hypothetico-Disjunctive Categorical.
Hypothetical Syllogism.— Canon.
(Oct. 1848). — Canon — Two or more propositions thought as in-
determined in quality, but as in quality mutually dependent, the
APPENDIX. 375
determination of quality in the one infers a determination of the
corresponding quality in the other.
This canon embodies and simpliiies the whole mystery of Hy-
pothetical Syllogisms, which have been strangely implicated, muti-
lated, and confused by the logicians.
1°, What are called Hypothetical Propositions and Syllogisms
are no more hypothetical than others. They are only hypothetical
as elliptical. When we say, If A is, then B is, we mean to say
the proposition, A is or is not, and the proposition, B is or is
not, are mutually dependent, — that as the one so the other. If here
only means taking for the nonce one of the qualities to the exclu-
sion of the other; I, therefore, express in my notation the connec-
tion of the antecedent and consequent of a hypothetical proposition,
thus : —
2°, The interdependent propositions are erroneously called Ante-
cedent and Consequent. Either is antecedent, either is consequent,
as we choose to make them. Neither is absolutely so. This error
arose from not expressing overtly the quantity of the subject of the
second proposition. For example, If man is, then animal is. In
this proposition, as thus stated, the negation of the first does not
infer the negation of the second. For man not existing, animal
might be realised as a consequent of dor/, horse, &c. But let us
consider what we mean ; we do not mean all animal, but so7ne
only, and that some determined by the attribute of rational iti/ or
such other. Now, this same some animal depends on man, and
7nan on it ; expressing, therefore, what we mean in the proposition
thus : — If all man is, then some animal is, — we then see the mutual
dependence and convertibility of the two propositions." For to say
that no animal is, is not to expKcate but to change the terms.
3°, The interdependent propositions may be dependent through
their counter qualities, and not merely through the same. For
example, As our hemisphere is or is not illuminated, so the other
is not or is ; hut the other is not illuminated; therefore ours is.
Another, If A is, then B is not; hut B is; therefore A is not.
<*■ Cf. Titius, Ars Cogltandi, c. xii. § lis, (1) iws'ito antecedente, ponitur conse-
26. " In specie falsum quoque arbitror, qiiens, non vero remoto antecedente, re-
quofl Syllogismi Conditionales duas ha- vioveturconsequens,{2)remotoco7}sequeiite,
beaut figuras, quae his muuiantur i-egu- removetur antecedens, non autem posito
376
APPENDIX,
Disjunctive and Hypothetical Syllogisms Proper.
Aristotle ignores these forms, and he was right. '^ His followers,
Theophrastus and Eudemus, with the Stoics, introduced them into
Logic as coordinate with the regular syllogism ; and their views
have been followed, with the addition of new errors, up to the pre-
sent liour. In fact, all that has been said of them has been wrong.
1°, These are not composite by contrast to the regular syllogism,
but more simple.
2°, If inferences at all, these are immediate and not mediate.
8°, But they are not argumentations but preparations (explica-
tions) for argumentation.^ They do not deal with the qufesitum, —
do not settle it ; they only put the question in the state required
for the syllogistic process ; this, indeed, they are frequently used
to sujDcrsede, as placing the matter in a light which makes denial or
doubt impossible ; and their own process is so evident that they
might, except for the sake of a logical, an articulate, development
of all the steps of thought, be safely omitted, as is the case with the
qusesitum itself For example : —
consequenfe, ponitur antecedens, . .
§ 28. Videamus specialius ; contra
primam regulam sic peccatur :
Si Chhienses sunt Mahometan!, sunt
infideles,
At non sunt Mali.ometani,
Ergo non sunt infideles,
" nam conclusio hie est absurda ! Ve-
rum si prsedicatum conclusionis sumatur
particulariter, nulla est absurditas, si
autem generaliter, turn evadunt quatuor
termini. § 9. Eodem exemplo secunda
regula etiam illustratur, sed assumemus
aliud ex Weisio, d. I.
Si miles est doctus, novit lihros (nempe
eicut eruditi solent).
Sed novit lihros (scil. ut alii homines,
etiam indocti, nosse solent).
Ergo miles est doctus.
" Hsec conclusio itidem pro falsa habe-
tur ! Sed jam indicavimus in addita
parenthesi veram causam, nempe qua-
tuor termino.s, quodsi autem medius
terminus eodem sensu accipiatur, ac in
syllogismo formaliter pi'oposito queat
minor probari, tum conclusio erit veris-
sima, idque virtute prscmissarum. § 30.
Omnis igitur error exinde habet ori-
ginem, quod quantitatem prsodicati vel
non intelligant, vel non observent ; si
igitur hunc lapsum evites, objecta ex-
empla omnia, qualia etiam Weisius d. I.
commemorat, facile dilues." — Ed.
a Cf. Titius, Ars Cogitandi, c. xii. § 7.
" SyllogismusDisjunctivus est en thyme-
ma sine majore, bis, oratione disjuncta
et positiva, propositum, . . . § 17.
Conditionalis seu Hypotheticus nihil
aliud est quam enthymema vel sine
majore, vel minore, bis, prima scil. vice,
conditionaliter, secunda, pure, proposi-
tum. § 20. Sequitur nullum peculiare
concludendi fundamentum vel formam
circa Syllogismos Conditionales occur-
rere, nam argumentationes imperfectas,
adeoque materiam syllogismorum regu-
larium illi continent." — Ed.
/3 This I say, for, notwithstanding
what M. St Hilaire so ably states in re-
futation of my paradox, I must adhere
to it as undisproved. — See his Transla-
tion of the Organon, vol. iv., p. 55.
APPENDIX. 877
1. Hypothetical (so called) Syllogism. Let the qusesitum or pro-
blem be, to take the simplest instance, — Does animal exist ? This
question is thus hypothetically prepared — If man is, animal is.
But [as is conceded] man is ; therefore, animal is. But here the
question, though prepared, is not solved ; for the opponent may
deny the consequent, admitting the antecedent. It, therefore, is
incumbent to show that the existence of animal follows that of
man, which is done by a categorical syllogism.
Animal, '»— - — : Man -. m , Existent.
2. Disjunctive (so called) Syllogism. Problem — Is John mortal?
Disjunctive syllogism — John is either mortal or immortal ; hut
he is not immortal ; ergo, [and this, consequently, is admitted as a
necessary alternative], he is mortal. But the [alternative ante-
cedent] may be denied, and the alternative consequent falls to the
ground. It is, therefore, necessary to show either that he is not
immortal, or, — the necessary alternative, — that he is mortal, which
is done by categorical syllogism.
John m^ , Man : »! : Immortal,
John m» Man : ■— , Mortal.
Hypothetical Infeeence.
Inasmuch as a notion is thought, it is thought either as existing
or as non-existing ; and it cannot be thought as existing unless it be
thought to exist in this or that mode of being, which, consequently,
affords it a ground, condition, or reason of existence. This is
merely the law of Reason and Consequent ; and the hypothetical
inference is only the limitation of a supposed notion to a certain
mode of being, by which, if posited, its existence is affirmed ; if
sublated, its existence is denied. For example, If A. is, it is B ; hut
A is, &c.
Again, we may think the existence of B (consequently of A B)
as dependent upon C, and C as dependent upon D, and so forth.
We, accordingly, may reason, //"A is B, and B is C, and C is D, &c.
Disjunctive Syllogism People.
(October 1848.) — Inasmuch as a notion is thought, it is thought
378 APPENDIX.
as determined by one or other, and only by one or other, of any
two contradictory attributes ; and in as much as two notions are
thought as contradictory, the one or the other, and only the one
or the other, is thought as a determiniug attribute of any other
notion. This is merely the law of Excluded Middle. The dis-
junctive inference is the limitation of a subject notion to the one or
to the other of two predicates, thought as contradictories ; the
affirmation of the one inferring the negation of the other, and
vice versa. As, A is either B or not B, &c. Though, for the
sake of brevity, we say A is either B or C or D, each of these
must be conceived as the contradictory of every other ; as, B = ]
C I D, and so on with the others.
Hypotheticals (Conjunctive and Disjunctive Syllogism).
(April 30, 1849). — These syllogisms appear to be only modifica-
tions or corruptions of certain immediate inferences ; for they have
only two terms, and obtain a third proposition only by placing
the general rule of inference, (stating, of course, the possible alter-
natives,) disguised, it is true, as the major premise. It is manifest
that we might prefix the general rule to every mediate inference ;
in which case a syllogism would have four propositions ; or, at
least, both j)reniises merged in one comj)lex j^roposition, thus —
If A and he either subject or predicate, [of the same term ?] tliey are
both subject or predicate of each other ;
But B is the subject of A and predicate of B [C ?] ;
.'. A is the jiredicate o/C-"
Thus, also, a common hypothetical should have only two proposi-
tions. Let us take the immediate inference, prefixing its rule, and
we have, in all essentials, the cognate hyj)Othetical syllogism.
] . — Conjunctive Hypothetical.
Aim is {some or all) A ; All men are (some) animals ;
Some or all B exists ; (All or some) men exist ;
Therefore, some A exists. Therefore, some animals exist.
a There seems to be an error here in hut B is A, and C is B; therefore, C is A.
the author's M.S. It is obvious that a This is apparently what the author
mediate inference may be expressed in means to express in a somewhat difFer-
the form of a hypothetical syllogism, ent form. — Ed.
Thus : // B is A, and C is B, then C is A;
APPENDIX. 379
Here it is evident that the first proposition merely contains the
general rule, upon which all immediate inference of inclusion
proceeds; to wit, that, the subjective part being, the subjective
whole is, &c.
Now, what is this but the Hj^othetical Conjunctive ?
If B is, A is ; If man is, animal is ;
But B is ; But man is ;
Therefore, A is. Therefore, animal is.
2. — Hypothetical Disjunctives.
B is either A or not A ; Man is either animal or non-
But B is A ; animal ;
Therefore, B is not not- A. But man is animal ;
Therefore, is not non-animal.
Stating this hypothetically, we may, of course, resolve the for-
mal contradictory into the material contrary. But this is wholly
extralogical.
Hypothetical and Disjunctive Syllogisms.
(1848 or 1849.) — The whole antecedent must be granted ; and
there cannot be two propositions inferred. In Categorical Syllo-
gisms, the antecedent is composed of the major and minor premises,
and there is only one simple conclusion, (though this may, in the
second and thu-d figures, vary). So in Hypothetical and Disjunc-
tive Syllogisms the whole antecedent is the two clauses of the
first proposition ; and the whole inference is the first and second
clauses of the second proposition, erroneously divided into minor
proposition and conclusion.
(January 1850.) — The Medium or Explicative may be indefinitely
various, according to the complexity of the Explicand ; and so may
the Explicate. The explicative and the explicate change places
in different exjilications. There is, in fact, no proper medium-
explicative or conclusion-explicate.
(January 18.50.) — In Disjunctives there is always at least double
the number of syllogisms (positive and negative) of the disjunct
members ; and in all syllogisms where the disjunct members are
above two, as there is thus afforded the possibility of disjunctive
380 APPENDIX.
explicates, there is another half to be added. Thus, if there be
two disjunct members, as A — x B C, there are four syllogisms,
but all of an absolute conclusion, — explicate. But if there be three
disjunct members, as A — x B C D, in that case there are six
absolute explicates, three positive and three negative, and, more-
over, three disjunctivo-positive conclusions, — explicates, after a ne-
gative explicative, and so on.
HiTPOTHETICAL SYLLOGISM.— CaNONS.
(February 1 850). — I. For Breadth, — The extensive whole or class
being universally posited or sublated, every subjacent part is posited
or sublated ; or for Depth, — All the comprehensive wholes being
posited or sublated, the comprehended parts are universally posited
or sublated.
II. For Breadth, — Any subjacent part being posited or sublated,
the extensive whole or class is partially posited or sublated ; or
for Depth, — Any comprehensive whole being posited or sublated,
the comprehended parts (or part) are, pro tanto, posited or sub-
lated, — Conversion and Restriction.
III. If one contradictory be posited or sublated, the other is
sublated or posited, — Contradiction.
IV. If some or a part only of a notion be posited or sublated,
all the rest (all other some) is sublated or posited — Integration.
V. If the same under one correlation be posited or sublated, so
under the other, — Equipollence.
VI. Law of Mediate Inference,« — Syllogism.
Mem. — The some in the explicand is, (as in the Conversion of
propositions), to be taken in the explicative as the same some.
There is thus an inference equally from consequent to antecedent,
as from antecedent to consequent.^
HYPOTHETICALS OR ALTERNATIVES.
Conjunctive, (Hypotheticals emphatically), and Disjunctive,
(Alternatives emphatically.)
(August 1852.)
Quantification, — A ny.
Affirmative, — Any, {Anything, Aught), contams under it every
a See above, p. 285.— Ed. j3 See above, p. 375. — Ed.
APPENDIX. 381
positive quantification, — All or Every, — Some at least, — Some
only, — This, These. (Best.)
Negative, — Not any, None, No, (Nothing, Naught), is equiva-
lent to the most exclusive of the negations, All not; All, or every
not; Not one, and goes beyond the following, which are only partial
negations, — Not all; Not some; Some not. (Worst.)
Affirmative, — Any, a highest genus and best ; not so Negative
— Not any^ — a lowest species, and worst. Therefore can restrict, —
subalternate in the former, not in the latter.
1 2
— Any, {all or every, — some). Some not, or not some, or not all-
^ ~ 'ZT' r: ' some only, (def)
rure ainrmative. v ":
Mixed affirmative and negative.
3
All or every not, not one, not any.
Pure negative.
If any {every) M he an (some) A, and any {every) A an {some) S, then is
any {every) M are S ; and v. v., if no {not any) A be any S, and any M
some A, then is no M any S.
.•. (On one alternative), some M bei7ig some A, and all A some S, some
M is some S.
(On the other), no A being any S, and every M so7ne A, no M is any S.
If, (on any possibility), M is, some A is ; or, v. v., if no A is, no M is.
.: (on one alternative), (in this actuality), some M being, some A is.
on the other), 7io A being, noM is.
Possible M : ,«-i — , A or A : ^ : M. Supposition of universal Pos-
sibiUty. In any case.
Actual M ,- » , A or A : » : A. Assertion of particular Actuality.
In this case.
From Possible, we can descend to Actual ; from Any, to Some ;
but Not any being lowest or worst, we can go [no] lower.
The Possible indifferent to Affirmation or Negation, it contains
both implicitly. But when we descend to the Actual, (and Poten-
tial ?), the two qualities emerge. This explains much in both
kinds of Hypotheticals or Alternatives, — the Conjunctives and
Disjunctives.
Higher classes, — Possible, Actual — Semjyer, quandocunque,
tunc, nunc — Ubicunque, ubique, ibi, hoc — Any, all, some, — In all,
every, any, case, in this case — Conceivable, real.
382 APrENDIX.
EuLEs OF Hypothetical Syllogisms.
1. Universal Rule of Restriction. — What is thought of all is
thought of some, — what is thought of the whole higher notion,
(genus), is thought of all and each of the lower notions, (special or
individual).
2. General Rule of both Hypotheticals. — What is thought (ira-
plictly) of all, the Possible, (genus), is thought (explicitly) of all
and each, the Actual, (species).
3. Special Rule of Conjunctives. — What is thought as consequent
on every Possible, is thought as consequent on every Actual, ante-
cedent.
4. Special Rule of Disjunctives. — What is thought as only Pos-
sible, (alternatively), is thought as only Actual, (alternatively).
5. Most Special Rule of Conjunctives
6. Most Special Rule of Disjunctives
Hypotheticals — Examples Unquantified.
(Higher to Lower.)
Affirmative. Negative.
If the germs is, the species is. If the genus is not, the species is not.
If the stronger can, the weaker can. If the stronger cannot, the weaker
cannot.
(Lower to Higher.)
If the species is, the genus is. If the species is not, the gemis is not.
If the weaker can, the stronger can. If the weaker cannot, the stronger
cannot.
(Equal to Equal.)
If triangle, so trilateral. If A he father of B, B is son of A;
iSicch poet Homer, such poet Virgil. .'. A heing father o/B, B is son of A ;
Where {when) the carcase is, there .'. B not being sou of A, A is not
{then) are the flies. father of B.
If Socrates he the son of Sop>hronis- If the angles he proportional to the
cus, Sop)hroniscus is the father sides of a A;
of Socrates. .'. An equiangular tv ill be an equi-
If equals he added to equals, the lateral A.
wholes are equal. If wheresoever the carcase is, there
will the eagles he gathered to-
gether. (Matth. xxiv. 28).
.'. If here the carcase is, here, &c.
APPENDIX. 383
A.) — Conjunctive Hypothetic als.
1). // A he D, it is A ; .-. { f ^'''f ;D, is A;
( A, not being A, **' ''O^ i) ;
/m o^Aer words, A is ez'iAer D o?' not A D.
Identity and Contradiction.
2). // B 6e A, it is not non-k ■ .: \ ^' f^("^ ^' '"V^".^ ''""f ^
; B, being non-A, is not A ;
In other words — B is either A or non-A.
Excluded Middle.
..\ rv-- -D 7 4 K .t • A } Vinotheinq A,isnon-A;
3). 7/ B be not A, it is non-A ;..(,. . ■ .
) B bemg non-A, is not A ;
III other words — B is either not A or not non-A.
Excluded Middle.
4). //E he not D, it is not A ■ .: \ S' f^^ ^^f9\i^ '^«^ ^ J
) E being A, is D ;
In other ivords — E is either not D A, or A D.
Contradiction and Identity.
b).— Disjunctive Hypotheticals.
// B he either A or non-A ■ .-. \ ^ ^''!'3 ^' *\^^? ^^'^f '
) B being non-A, is not A.
Excluded Middle.
" i/" means suppose that, — in case that, — on the supposition —
— hypothesis — under the condition — under the thought that, — it
being supposed possible ;
.'. &c., means then, — therefore, — in that case, &c., &c. — in
actuality eithei\
Only, properly, in botli Conjunctives and Disjunctives, two con-
tradictory alternatives. Por contrary alternatives only material,
not formal, and, in point of fact, either A or B or C means A or
non-A., B or woh-B, C or non-C.
The minor premise, on the common doctrine, a mere materi-
ality. Formally, — logically, it is a mere differencing of the conclu-
sion, which is by formal alternative aflbrded.
384 APPENDIX.
1.) In Hypotlieticals, (Conjunctive and Disjunctive), two or three
hypotheses. The first is in the original supposition of possibi-
lity. {If B be A, it is not non-A — If B be eitJie?' A or non-A).
The second (and third) is in the alternative suppositions of actua-
lity (.•. either if B be A, it is not non-A, or if B be non-A, it is
not A. — .•. If B be A, it is not non-A, or if B be non-A, it is not
A). (Possibly, — by possible supposition) If man is, animal is;
.: (actually) Man being, animal is; (or) animal not being, man
is not.
1). Possibility — a genus indifferent to negative and affirmative.
These two species of Possibility, to wit two Actuals, — an actual yes
and an actual no. The total formal conclusion is, therefore, of
two contradictories. This explains why, in Conjunctive and Dis-
junctive Hypotheticals, there are two alternative consequents, and
only one antecedent.
2). In Hypotheticals (Conjunctive and Disjunctive) a division of
genus in the first supposition into two contradictories, — species.
The inference, therefore, one of subalternation or restriction.
3). In Hypotheticals, (Conjunctive and Disjunctive), two alter-
native contradictory conclusions — the form giving no preference
between the two, the matter only determining, (other immediate
inferences have only one determinate conclusion, and all mediate
syllogism has virtually only one). Formally, therefore, we cannot
categorically, determinately, assert, and assert exclusively, either
alternative, and make a minor separate from the conclusion. This
only materially possible ; for we know not, by the laws of thought,
whether a certain alternative is, knowing only that one of two
alternatives must be. Formally, therefore, only an immediate
inference, and that alternative double.
4). Hypothetical, (Conjunctive and Disjunctive), reasoning more
marking out, — predetermining, how a thing is to be proved
than proving it.
5). Thus, three classes of inference : 1°, Simple Immediate In-
ference. — 2°, Complex Immediate Inference, (Hypotheticals Con-
junctive and Disjunctive). — 3°, Syllogisms Proper, Mediate Infer-
ence.
6). If we quantify the terms, even the formal inference breaks
down.
7). The only difference between the first proposition and the
APPENDIX. 385
two latter, is the restriction or subalternation. These last should,
therefore, be reduced to one, and made a conclusion or restriction.
The genera and species are of the most common and notorious
kinds, as Possible and Actual, — Wherever, Here, &c. — Whenever,
Noio, — All or Every, Some, This, &c. The commonness and noto-
riety of this subordination is the cause why it has not been sig-
nalised ; and if signalised, and overtly expressed, Hypotheticals
might be turned into Categoricals. It is better, however, to leave
them as immediate inferences. For it would be found awkward
and round-about to oppose, for example, the Possible to the
Actual, as determining a difference of terms. (See Molinseus, Mem.
Log., L. i. tr. iii. p. 95, and Pacius, In Org., De 8yll. Hyp., p. 533.)
The example of the Cadaver there given, shows the approximation
to the ordinary Hypotheticals. They may stand, in fact, either for
Categoricals or Hypotheticals.
8). Disjunctives — (Possibly) A is cither B or non-'^ ; .'. (Actu-
ally) A is cither, &c.
9). The doctrine in regard to the Universal Quantity, and the
Affirmative Quality (see Krug, Loejih, §§ 57, 83, 86, pp. 171, 264,
275), of the supposition, proposition, of Conjunctive (?) and Dis-
junctive Hypotheticals, is solved by my theory of Possibility. In
it is virtually said, (whatever quantity and quality be the clauses) —
" on any possible supposition." (On the Quality v. Krug, Logih, §
57, p. 172. Pacius, In Org., p. 533. Molin?eus, Eleiii. Log., I. c.)
10). Possibly, — problematically includes as species the actual
affirmative, and the actual negative. It will thus be superfluous
to enounce a negative in opposition to an affirmative alternative ;
for thus the possible would be brought down to the actual ; and
the whole syllogism be mere tautological repetition.
11). The quantified terms, if introduced, must either be made
determinate, to suit the Hj^otheticals, or must ruin their infer-
ence. Por example — If all or some man be some animal, we
must be able to say. But some animal is not, therefore man
{any or some) is not. But here some animal, except definitised
into the same some animal, would not warrant the required infer-
ence. And so in regard to other quantifications, which the logicians
have found it necessary to annul.
12). The minor proposition may be either categorical or hypo-
thetical. (See Kj-ug, Logik, § 83, p. 264. Heerebord, Instit.
VOL. II. 2 B
386 -APPENDIX.
Logicar. Synopsis, L. ii. c. 12, pp. 266, 267.) In my way of stat-
ing it : — If man is,- animal is, .: If man is (or ma7i being),
animal is.
13). Of notions in the relation of sub-and-superorclination, (as,
in opposite ways Depth and Breadth, Containing and Contained),
absolutely and relatively, the lower being affirmed, the higher are
(partially) affirmed ; and the higher being (totally) denied, the
lower are (totally) denied. A, E, I, O, U, Y may represent the
descending series.
The first proposition is conditional, complex, and alternative ;
we should expect that the second should be so likewise. But this
is only satisfied on my plan ; whereas, in the common, there is a
second and a third, each categorical, simple, and determinate.
The subalternation is frequently double, or even triple, to wit,
1 °, From the Possible to the Actual. 2°, (for example) From every-
where to hei'e, or this place, or the place by name. 3°, From all
to some, &c. — in fact, this inference may be of various kinds.
The [xeTaXr]\l/L<s of Aristotle may mean the determination, — the
subalternation ; the Kara TroioTiqra may refer to the specification
of a particular quality or proportion under the generic ; and the
Trpoa\iq^i<i of Theophrastus (for the reading in Aristotle should
be corrected) may correspond to the Kara TTOLOTTjTa.
There is no necessary connection, formally considered, between
the antecedent and consequent notions of the Hypothetical major.
There is, consequently, no possibility of an abstract notation ; their
dependence is merely supposed, if not material. Hence the logi-
cal rule, — Propositio conditionalis nihil ponit in esse. (See Krug,
Logik, § 57, p. 166.) But on the formal supposition, — on the case
thought, what are the rules ?
We should distinguish in Hypotheticals between a propositional
antecedent and consequent, and a syllogistic A and C ; and each
of the latter is one proposition, containing an A and C.
The antecedent in an inference should be that which enables us
formally to draw the conclusion. Show in Categoricals and in
Immediate Inferences. On this principle, the conclusion in a
APPENDIX. 887
Hypothetical will contain what is commonly called the minor
proposition with the conclusion proper ; but it will not be one and
determinate, but alternative.
If there were no alternation, the inference would follow imme-
diately from the fundamental proposition ; and there being an al-
ternative only makes the conclusion alternatively double, but does
not make a mediate inference.
To make one alternative determinate is extralogical ; for it is
true only as materially proved. 1'^, The splitting, therefore, of the
conclusive proposition into two, — a minor and a conclusion proper,
is wholly material and extralogical ; so also, 2°, Is the multiply-
ing of one reasoning into two, and the dividing between them of
the alternative conclusion.
Errors of logicians, touching Hypothetical and Disjunctive Rea-
sonings : —
1°, That [they] did [not] see they were mere immediate infer-
ences.
2°, Most moderns that both Hypothetical.
3°, That both alternative reasonings in one syllogism.
4°, Mistook a part of the alternative conclusion for a minor
premise.
5°, Made this a distinct part, (minor premise), by introducing
material considerations into a theory of form.
6°, Did not see what was the nature of the immediate inference
in both, — how they resembled and how they differed.
B.-HISTORICAL NOTICES.
(Conjunctive and Disjunctive.)
I. Aristotle.
(August 1852.)
Aristotle, {Anal. Pr. L. i. c. 32, § 5, p. 262, Pacii,) describes the
process of the Hypothetic Syllogism, (that called by Alexander
St' o\(ov), but denies it to be a syllogism. Therefore his syllogisms
from Hypothesis are something different. This has not been no-
ticed by Mansel, Waitz,
Thus literally : — " Again, if man existing, it be necessary that
388 APPENDIX.
animal exist, and if animal, that substance ; man existing, it is
necessary that substance exist. As yet, there is, however, no syl-
logistic process ; for the propositions do not stand in the relation
we have stated. But, in such like cases, we are deceived, by reason
of the necessity of something resulting from what has been laid
down ; whilst, at the same time, the syllogism is of things neces-
sary. But the Necessary is more extensive than the Syllogism ;
for though all syllogism be indeed necessary, all necessary is not
syllogism." Why not? 1°, No middle. 2", No quality, — affirma-
tion or negation ; problem, also not assertory, — hypothetical not
syllogistic. 3°, No quantity. Compare also An. Pr. L. i. c. 24.
Aristotle, {Anal Post, L. i. c. 2, § 15, p. 418 ; c. 10, §§ 8, 9,
p. 438) makes Thesis or Position the genus opposed to Axiom,
and containing under it, as species, \°, Hypothesis or Supposition ;
and, 2°, Definition. Hypothesis is that thesis which assumes
one or other alternative of a contradiction. Definition is that
thesis which neither affirms nor denies. Hypothetical, in Aris-
totle's sense, is thus that which affirms or denies one alternative
or other, — which is not indifferent to yes or no, — which is not
possibly either, and, consequently, includes both. Hypotheticals,
as involving a positive and negative alternative, are thus, in Aris-
totle's sense, rightly named, if divided ; but, in Aristotle's sense,
as complete, they are neither propositions nor syllogisms, as not
affirming one alternative to the exclusion of the other."
II. — Ammonius Heemi^.
I. Ammonius Hermiae, on Aristotle Of Enounceinent, Intro-
duction, f 3. ed. Aid. 1546, f 1. ed. Aid. 1503. After distinguish-
ing the five species of Speech, according to the Peripatetics, —
o [Whether the Syllogisms ex Hypo- Tract. Si/ll. P. iv. c. x. tit. 2, p. 548. Burs-
thesi of Aristotle are correapondent to gersdicius, Instit. Log. L. ii. cc. 12, 14,
the ordinary Hypothetical Syllogism. pp. 263, 270, 275. Ritter, Gesch. der
For the affirmative, see Pacius, Com. Phil. iii. p. 96. (Eng. Tr., p. 80),
in Org. An. Prior., L. i. cc. 23, 29, 44, Ramus, Sckoke Dial. L. vii. cc. 12, 13,
pp. 153, 177, 194, St Hilaire, Transla- pp. 492, 503. Molinasus, Elementa Lo-
tion of Organon, vol. ii. pj). 107, 139, gica, p. 95 et seq. Waitz, Org. i. pp.
178. 427,433. Ci. Alexander, In An. Prior.,
For the negative, see Piccartus, In S. 88, 109. Philoponus, In An. Prior.,
Org.An. Prior,h. I 00.40,4:1, 42, p. 5Q0. ff. 60'\ 60", 87", 88. Anonymus, Be
Neldelius, Be Usu Org. Arist. P. iii. c. 2, Syllogismo, f. 44''. Magentinus, In An.
pp. 38, 45., (1607.) Keckermanu, Opera, Prior., i. 17". Ammonius, In de Interp.,
pp. 766, 767. Scheibler, Oj^era Logica 3'\ Blemmidas, Epit. Log. c. 36.]
APPENDIX. 889
the Vocative, the Imperative, the Interrogative, the Optative, and
the Enunciative or Assertive, — having further stated the corres-
ponding division by the Stoics, and having finally shown that
Aristotle, in this book, limited the discussion to the last kind, that
alone being recipient of truth and falsehood, he thus proceeds : —
"Again, oi Assertive speech, [aTTocfiavTLKOv \oyov), there are two
species ; the one called Categoric [or Predicativel, the other
Hypothetic [or Suppositive]. The Categoric denotes, that some-
thing does or does not belong to something : as when we say,
Socrates is walking, Socrates is not walking; for we predi-
cate lualking of Socrates, sometimes affirmatively, sometimes nega-
tively. The Hypothetic denotes, that something being, something
[else] is or is not, or something not being, something [else] is
not or is : As when we say, If man be, animal also is, — If he
be man, he is not stone, — If it be not dag, it is night, — If it be
not day, the sun has not risen.
" The Categoric is the only species of Assertive speech treated
of by Aristotle, as that alone perfect in itself, and of utility in
demonstration ; whereas Hypothetic syllogisms, usurping [usually]
without demonstration the [minor] proposition, called the Tran-
sumption, or Assumption, and sometimes even a [major premise]
Conjunctive or Disjunctive, requiring proof, draw their persuasion
from hypotheses, should any one [I read et rtg for 17x1?,] con-
cede their primary suppositions. If, then, to the establishment of
such suppositions, we should employ a second hypothetic syllo-
gism, — in that case, we should require a further establishment
for confirmation of the suppositions involved in it ; for this
third a fourth would again be necessary ; and so on to infinity,
should we attempt by hypotheses to confirm hypotheses. But
to render the demonstration complete and final, it is manifest
that there is needed a categoric syllogism to prove the point in
question, without any foregone supposition. Hence it is, that
Categoric [reasonings] are styled Syllogisms absolutely ; whereas
Hypothetic [reasonings] of every kind are always denominated
Syllogisms from hypothesis, and never Syllogisms simply. Add
to this, that Hypothetic enouncements are made up of Categoric.
For they express the consequence or opposition [aKokovdiav rj
Siacrracrti') of one Categoric proposition and another, uniting
them with each other, by either the Conjunctive or Disjunctive par-
390 APPENDIX.
tide, {(TV[X7r\eKTLK(^ ^ Sta^evKxtKoi avvSeajxcp), in order to
sliow that they constitute together a single enouncement. For
these reasons, therefore, Aristotle has only considered, in detail,
the Categoric species of Assertive speech."
III. — Anonymous Scholion.''
In Hypothetic Syllogisms, the first [I] are those of two terms,
[a] Conjunctive, or [b] Disjunctive, {opot ol avvrjixixevoL r) Sta-
XeXv/xeVot) ; then follow [II] the two [classes of] syllogisms with
three, and these conjunctive terms.
[I. a]. " There are four syllogisms through the Return (17 ctt-
dvoSos) on the prior (6 7rp6Tepo<i, 6 irpoiTO';) [or antecedent clause
of the hypothetical proposition], and four through it on the pos-
terior (6 ^evTepo^;, 6 ea^aTO'^). For the terms are taken, either both
affirmatively or both negatively. And the return upon the prior is
ponent {Kara Oiaiv) upon the posterior tollent [Kara avaipeaiv.
For example [the return upon the prior] : —
(1). If A is, B is ; (Return) but A is; {Conclusion, o-v/xirepaa-na) ikerefore,
Bis.
(2). If A is, B is not ; but A is ; therefore, B is not.
(3). If A is not, B is ; hit A is not, therefore, B is.
(4). If A is not, B is not : but A is not ; therefore, B is not,
" The return upon the posterior : —
(1). If A is, B is ; but B is 7iot ; therefore, A is not.
(2). If A is, B is not ; but B is ; therefore, A is not.
(3). If A is not, B is ; but B is not ; therefore, A is.
(4). If A is not, B is not ; but B is ; therefore, A too is.
[b.] " Following those of conjunctive, are syllogisms of disjunc-
tive, terms. In these, the return is upon either [clause] indifferently.
For example : If it must he that either A is or B is ; [in the one
case], B is not, therefore, A is ; or, [in the other], A is not, there-
fore B {5.
[II.] " Of three conjunctive terms, there are [in the figures taken
together] eight syllogisms, through a return on the prior, and eight
[sixteen] P through a return on the posterior [clause]. For the
a lu Waitz, Org. i., pp. 9, 10. placed first, according to the common
jS It would seem that the author here, practice of the Greeks, or the major
and in the last sentence, discounts alto- prior, in Aristotelic theory), he should
gether the first figure, puzzled, appa- accord the designation of first,
rently, to which premise, (the minor
APPENDIX. 391
three terms are correlated (o-vvTiOevTaC), either all affirmatively,
or some ; and here either the third alone, or the third and second,
or the second alone, negatively. Again, either all are negatively
correlated, or some ; and here either the third alone, or the third
and second, or the second alone, affirmatively. In this manner
the correlation [in each figure] is eightfold ; taking for exemplifi-
cation only a single mood [in the several figures] : —
If A is, B is :
7/'B is, C is ;
If A is, there/ore, G is.
This is of the first figure. Por the middle coUative term
(6 (rvuayoju opo<^ fxecrog) is twice taken, being the consequent
(6 XTJycou) in the former conjimctive [premise] {to irpoTcpov
crvvr)fMjJieuop), the antecedent (6 -qyovixevoi) in the latter. Where-
fore, these syllogisms are indemonstrable," not requiring reduction
(t) avaXvcTLS;) for demonstration. The other moods of the first
figure are, as has been said, similarly circumstanced.
" The second figure is that in which the collative term [or
middle] (6 crvpaycov) holds the same relation to each of the col-
lated [or extreme] terms, inasmuch as it stands the antecedent of
both the conjunctive [premises], except that in the one it is affirm-
ative; in the other, negative. Wherefore, when reduced to the
first figure, they demonstrate, as is seen, through the instance of a
single mood composed of affirmative collated terms. As : —
If A is, B is;
If A is not, C is ;
IfB is not, therefore, C is.
" This is reduced to the first figure in the following manner : —
"Whether it has the collated terms, both affirmative, or both nega-
tive, or both dissimilar to the reciprocally placed collative term,
there is taken in the reduction the opposite [and converse] of the
prior conjunctive [premise] ; and the latter is applied, in order
that the opposite of the consequent in the former conjunctive [pre-
mise] may find a place in the foresaid mood. As : —
If B is not, A is not ;
If A is not, G is ;
If'Bisnot,the7'efo7r,Gis.
" This it behoved to show.
» Vide Apuleius. [De. Dorjm. Plat. iii. p. 37. Elm. Cf. Discussions, -p. 836.— Ed.]
392 APPENDIX.
" The third figure is that in which the collative terra holds the
same relation to each of the collated terms, being the consequent
in either conjunctive [premise] afiirmatively and negatively, as in
the example of a single mood again consisting of affirmative col-
lated terms. Thus :—
If A. is, B is ;
7/C is, B is not ;
If A. is, therefore, C is not.
"The reduction of this to the first figure is thus effected. The
opposite [a converse E] of the second conjunctive [premise] is
taken along with the first conjunctive [premise], and the ante-
cedent of the former is appHed to the opposite of the latter's con-
sequent ; as in the foresaid mood. Thus : —
If A is, B is ;
IfB is, C is not ;
If A is, therefore, C is not.
" All this requires to be shown concretely. As in the first figure
[first mood] : —
If day is, light is ;
If light is, visible objects are seen ;
If day is, therefore, visible objects are seen.
" Second figure, first mood :
If day is, light is ;
If day is not, the sun is under the earth ;
If light is not, the sicn is [therefore], under the earth.
" Eeduction :
//' liffht is not, day is not ;
If day is not, the sun is under the earth ;
If light, therefore, is not, the sun is under the earth.
" Third figure, first mood :
If day is, light is ;
If things visible are unseen, light is not ;
If day, therefore, is, things visible are not tinseen.
" There are eight moods of the second figure, and eight of the
third ; two composed of affirmatives, two of negatives, four of dis-
similars, with a similar or dissimilar collative.
" End of Aristotle's Analytics."
APPENDIX. 893
Eelative to the translation from the Greek interpolator on
Hypothetical Syllogisms, in Waitz, {Org. \., pp. 9, 10) ; and in
particular to the beginning of [IL]
Better thus : — In all the Figures : — the quality of the syllogism
is either Pure, — and here two, viz., one affirmative and one nega-
tive ; or Mixed, — and here six, viz., three in which affirmation, and
three in which negation, has the preponderance.
The following are thus arranged : —
First Figure. Second Figure. Third Figure.
' ^ All If A is, B is ; If B is, A is ; If A. is, B is ;
p* A // B is, C is ; If B is, C is ; If C is, B is;
fe .'. If K is, C is. .-. If A is, C is. .'. If A is, C is.
a
I 1,2 If A is, B is : If B is, A is ; If A is, B is ;
S. B // B is, C is not ; If B is, C is not ; If C is not, B is ;
"£ .'. If A is, C is not. .•. If A is, C is not. .'. If A is, C is not.
&
g 1> 3 If A is, B is not ; If B is not, A is ; If A is, B is not:
•2 C IfB is not, C is ; If B is not, C is ; If C is, B is not ;
g .'.If A is, C is. ,'. If A is, C is. .". If A is, C is.
y^ 2,3 If A is not, B is ; If B is, A is not ; If A is not, Bis ;
^ IfB is, C is J If B is, C is ; If C is, B is ;
.•. If A is not, C is. .'. If A is not, C is. .'■ If A is not, C is.
All If A is not, B is not. If B is not, A is not ; If A is not, B is not ;
E If B is not, C is not ; If B is not, C is not ; If C is not, B is not ;
.•. If A is not. C is not. .-. IfB is not, C is'not; •'■ If A is not, C is not.
1)2 /y A is not, B is not ; If B is not, A is not. If A is not, B is not.
F IfB is not, C is ; If B is not, C is ; If C is, B is not ;
.: If A is not, C is. .-. // A is not, C is. •'■ If -^ is ^'of, C is.
1 ' ^ If A is not, B is ; If B is, A is not ; Jf A is not, B is ;
^ IfB is, C is not ; If B n, C is not ; If C is not, B is ;
.•. If A is not, C is not. .'. If A is not, C is not. .-. If A is not, C is not.
m
2, 3 If A is, B is not ;
IfB is not, A is;
H IfB is not, C is not;
IfB is not, C is not ;
.: If A is, C is not.
.'.If A is, C is not.
^ 2, 3 // A is, B is not ; If B is not, A is ; If A is, B is not ;
If C is not, B is not ;
.: If A is, C is not.
These eight syllogisms are all affirmative, the negation not being
attached to the principal copula.* If, therefore, the negation be
a See Lovanienses, In Arist. Dial, Tract, de Hypotheticis Syllogismis, p. 299.
394
APPENDIX.
attached to one or other premise, there will be sixteen negative
syllogisms, in all twenty-four. The negatives are, however, awk-
ward and useless. — (See Lovanienses, p. 301.)
But each of these twenty-four syllogisms can receive twelve,
different forms of predesignation, corresponding to the twelve moods
of the simple categorical ; according to which they are arranged
and numbered. It is hardly necessary to notice that the order
of the premises is in Comprehension, after the Greek fashion of the
scholiast.
i.
ii.
ill.
iv.
V.
vi.
vii.
viii.
ix.
X.
xi.
xii.
TA
>
J
:
>
)
>
:
>
'
MB
> •
• )
J •
• 5
> •
• J
} •
• 5
CC
}
>
'
••
>
:
>
5
>
This is exemplified in the Syllogism E of the preceding table,
thus :
1. IfciJl A is not, all B is not ; if all B is not, all C is not ; .". if all A
is not, all B is not,
2. If some A is not, all B is not ; if all B is not, some C is not ; .'. if
some A is not, someG is not.
3. If some A. is not, all B is not; if all B is not, all C is not ; .: if some
A is not, all C is not.
4. If all A is not, all B is not ; if all B is not, some C is not ; .: if all
A is not, some C is not.
5. If all A is not, some B is not ; if all B is not, all C is not ; .'. if all
A is not, all C is not.
6. If some A is not, all B is not ; if some B is not, all C is not ; .: if
some A is not, all C is not.
7. If all A is not, some B is not ; if all B is not, some C is not ; .'. if all
A is not, some G is not.
8. If some A is not, all B is not ; if some B is not, all G is not ; .'. if some
A is not, all G is not.
9. If some A is not, some B is not ; if all B is not, all G is not; .'. if
some A is not, all G is not.
10. If all A is not, all B is not ; if some B is not, some G is not ; .: if all
A is not, some G is not.
11. If some A is not, some B is not; if all B is not, some G is not; .'. if
some A is not, some G is not.
12. If some A is not, all B is not; if some B is not, some G is not ; .'. if
some A is not, some G is not.
APPENDIX. 895
IX.
SORITES.
See above, Vol. I., p. 385.)
(Without order.)
All logicians have overlooked the Sorites of Second and Third
Figures.
In Sorites of the Second or Third Figure, every term forms a
syllogism with every other through the one middle term. In
Sorites of the Fii-st Figure, every Second term at most forms a
syllogism with every other, through its relative middle term.
No subordination in Sorites of Second or Third Figure, ergo
no one dominant conclusion.
Alias In First Figure, there being a subordination of notions,
there may be a Sorites with different middles, (all, however, in a
common dependency). In Second and Thu'd Figures, there being-
no subordination of terms, the only Sorites competent is that by
repetition of the same middle. In First Figure, there is a new
middle term for every new j)rogress of the Sorites ; in Second and
Third, only one middle term for any number of extremes.
In First Figure, a Syllogism only between every second term of
the Sorites, the intermediate term constituting the middle term.
In the others, every two propositions of the common middle term
form a syllogism.
Alias — There being no subordination in Second and Third
Figures between the extremes, there, consequently, are —
1°, No relations between extremes, except through the middle
term.
2°, There is only one possible middle term ; any number of others.
3°, Every two of the terms, with the middle term, may form a
syllogism.
4", No order.
Before concluding this subject, I would correct and amplify the
doctrine in regard to the Sorites."
1°, I would state that, by the quantification of the Predicate, (of
« luterpciliitiun ill Zec<i«'cs. See above, Vol. I., p. 385. — Ed.
396 APPENDIX.
which we are hereafter to treat, in reference to reasoning in
general), there are two kinds of Sorites ; the one descending from
whole to part, — or ascending from part to whole ; the other pro-
ceeding from whole to whole ; of which last it is now alone requi-
site to speak. It is manifest, that if we can find two notions
wholly equal to a third notion, these notions will be wholly
equal to each other. Thus, if all trilateral figure be identical with
all triangular figure, and all triangular figui-e with all figure the
sum of whose internal angles is equal to two right angles, then all
figure, the sum of whose internal angles is equal to two right
angles, and all trilateral figure, will also be identical, reciprocating,
or absolutely convertible. We have thus a simple syllogism of
absolute equation. On the same principle, if A and B, B and C,
C and D, are absolutely equivalent, so also will be A and D. We
may thus, in like manner, it is evident, have a Sorites of absolute
equivalence. It is not, indeed, very easy always to find four or
more terms or notions thus simply convertible. In geometry, we
may carry out the concrete syllogism just stated, by adding the
three following propositions ; — All figure, the sum of whose inter-
nal angles is equal to two rigid angles, is all figure which can he
bisected through only one angle ; — All figure which can he hisected
through only one angle, is all figure which, hisected through an
angle and a side, gives two triangles ; and All figure which, thus
hisected, gives two triangles, is all figure which, hisected through
two sides, gives a triangle and a quadrangle, and so forth. In
theology, perhaps, however, these series are more frequently to be
found than in the other sciences. The following twelve equivalent
concepts constitute at once a good example of such a Sorites, and
at the same time exhibit a compendious view of the whole Calvin-
istic doctrine. These are, — 1. Elected — 2. Redeemed — 3. Called —
4. Graced with true repentance — 5. With true faith — 6. With
true personal assurance — 7. Pardoned — 8. Justified — 9. Sancti-
fied — 10. Endoiued with jier severance — 11. Saved — 12. Glorified.
This series could indeed be amplified ; but I have purposely re-
stricted it to twelve. Now, as All the elect are all the redeemed,
all the redeemed all the called, all the called all the [truly]
penitent, all the [tridy] penitent all the [truly'] helieving, all the
[tr'idy] helieving all the [truly] assured, all the [truly] assured
all the pardoned, all the ixirdoned all the justified, all the justi-
I
I
APPENDIX.
397
Hed all the sanctified, all the sanctified all the perseverant, all
the jjersevei'ant all the saved, all the saved all the glorified,
all the glorified all the blest with life eternal ; it follows, of ne-
cessity, that all the blest tuith life eternal are all the elect. To
turn this affirmative into a negative Sorites, we have only to say,
either at the beginning, — None of the reprobate are any of the
elect, and, consequently, infer, at the end, that none of the blessed
with eternal life are any of the reprobate ; or at the end, — Kone of
the blessed with eternal life are any of the punished, and, conse-
quently, infer that none of the punished are any of the elect. Per-
haps the best formula for this kind of Sorites is to be found in the
letters a, b, c. This will afford us a Sorites of six terms, viz., a,
b, c — a, c, b — b, a, c — b, c, a — c, a, b — c, b, a — which are all vir-
tually identical in their contents. If there be required a formula
for a longer Sorites, we may take the letters a, b, c, d, which will
afford us twenty- four terras. Perhaps the best formula for a de-
scending or ascending Sorites is, for example, a, b, o, d, e, f — a, b,
c, d, e, — a, b, c, d, — a, b, c, — a, b, — a.
I. — COMPREHENSIVE SORITES — PROGRESSIVE AND REGRESSIVE.
E
Bucephalus
A
, Substance
II. — EXTENSIVE SORITES.
398 APPENDIX.
X.
SYLLOGISM.
A-ITS ENOUNCEMENT— ANALYTIC AND SYNTHETIC-
ORDER OF PREMISES.
(See above, Vol. I., p. 395.)
(a) ENOUNCEMENT OF SYLLOGISM.
(Nov. 1848.) — There are two orders of enouncing the Syllogism,
both natural, and the neglect of these, added to the not taking
into account the Problem, or Question, has been the ground why
the doctrine of syllogism has been attacked as involving a petitio
yrincipii, or as a mere tautology. Thus, Buffi er cites the defi-
nition the art of confessing in the conclusion what has been al-
ready avowed in the premises."- This objection has never been
put down.
The foundation of all syllogism is the Problem. But this may
be answered either Analytically or Synthetically.
I. Analytically (which has been wholly overlooked) thus, — Pro-
blem or qupesitvim, Is V Ci Answer, V is G; for V is M, and
M is C. This in the reasoning of Depth. More explicitly : — Does
r contain in it Cl T contains in it C ; for T contains in it M,
and M contains in it C. But it is wholly indifferent whether we
cast it in the reasoning of Breadth. For example : — Does C con-
tain under tY F ? C contains under it F ; for C contains under
it M, and M contains under it F-/3
Here all is natural ; and there is no hitch, no transition, in the
order of progressive statement. The whole reasoning forms an
organic unity ; all the parts of it being present to the mind at
once, there is no before and no after. But it is the condition of a
verbal enouncement, that one part should precede and follow
another. Here, accordingly, the proposition in which the reason-
aSeconde Lor/ique, Art. iii. § 126. — thenthemmor, {that [/oodme7i so think);
Ed. lastly the major, {that the presentiments
y3 Plato, in a letter to Dionysius, {Epist. of divine men are of highest authority).
2), reverses the common order of Syllo- Platonis Opera, Bekker, ix. p. 74. Cf.
gism, placing the conclusion first, {that Melanchthon, Dialectica, L. iii., De Fig-
he thinks there is some sense in the dead) ; uratione, p. 93, ed. 1542.
APPENDIX. 399
ing is absolved or realised, and which, from the ordinary mode of
enomiceraent, has been styled the Conclusion, is stated first ; and
the gromids or reasons on which it rests, which, from the same cir-
cumstance, have been called the Premise ov Antecedent, are stated
last. This order is Analytic. We proceed from the effect to the
cause, — from the principiatum to the principia. And it is evident
that this may be done indifferently either in Depth or Breadth ;
the only difference being that in the counter quantities the grounds
or premises naturally change their order.
II. Synthetically ; — the only order contemplated by the logicians
as natm^al, but on erroneous grounds. On the contrary, if one
order is to be accounted natural at the expense of the other, it is
not that which has thus been exclusively considered. For —
1°, It is full of hitches. There is one great hitch in the separa-
tion of the conclusion from the question ; though this latter is
merely the former proposition in an assertive, instead of an inter-
rogative, form. There is also at least one subordinate hitch in
the evolution of the reasoning.
2°, The exclusive consideration of this form has been the cause or
the occasion of much misconception, idle disputation, and ground-
less objection.
(On the two Methods ; tumultuary observations, to be better
arranged, and corrected.)
I'', In the first or analytic order, what is principal in reality and
in interest, is placed first, that is, the Answer or Assertion, called on
the other order the Conclusion.
2°, In this order all is natural ; there is no hitch, no saltus, no
abrupt transition ; all slides smoothly from first to last.
a) The question slides into its answer, interrogation demands
and receives assertion.
b) Assertion requires a reason and prepares us to expect it ;
and this is given immediately in what, from the other order, has
been called the Antecedent or Premises.
c) Then the first term, either in Breadth or Depth, is taken first
in the ground or reason, and compared with M ; then M is com-
pared with the other. As in Breadth ; — Does C contain under it
r ? C contains T ; for C contains under it M, and M contains
under it V. — In Depth — Does V contain in it C? T contains in
400 APPENDIX.
it C ; for T contains in it M, and M contains in it C. Tliis is the
first Figure. — Second Figure, using common language : — Is F C ?
r is C (and C is T) ; for T and C are both the same M. Here
the two extremes taken together are compared with M. — In the
Third Figure M is compared with both extremes — Is F C ? V is
C {and M is Y) ; for the same M is both V and C.
3°, In this order there is nothing pleonastic, nothing anticipated.
4° Nothing begged.
- 5°, In this method the process is simple. Thought is one ; but
to be enounced it must be analysed into a many. This order
gives that necessary analysis, and nothing more.
6°, In this order, when assertive, answer is limited by ques-
tion ; good reason why, in Second and Third Figures, one answer
should be given.
7", This order is the one generally used by the mathematicians.
(See Twesten, Logik, inshesondere die Analytik, § 117, p. 105,
and below, p. 405. Plato also).
8°, If the Qusesitum be stated as it ought to be, this order
follows of course ; and the neglect of the qusesitum has followed
from the prevalence of the other. If the qufesitum be stated in
using the common form, we must almost of course interpolate a
yes or a no before proceeding to the premises in the common
method ; and, in that case, the conclusion is only a superfluous
recapitulation.
In the Synthetic, or common order, all is contrary. (The num-
bers correspond.)
1°, In this order, what is first in reality and interest, and in
and for the sake of which the whole reasoning exists, comes last ;
till the conclusion is given we know not, (at least we ought not to
know), how the question is answered.
2°, In this order all is unnatural and contorted by hitches and
abrupt transitions. There is no connection between the question
and what prepares the answer, — the premise. (Show in detail.)
3°, In this order all is pleonastic and anticipative. The pre-
mises stated, we already know the conclusion. This, indeed, in
books of Logic, is virtually admitted, — the conclusion being com-
monly expressed by a therefore, &c. Ancient doctrine of Enthy-
meme, (Ulpian,&c.), unknown to our modern logicians; among their
APPENDIX. 401
other blunders on the Enthymeme. On the common doctrine,
Logic, — Syllogistic, — is too truly defined the art of confessing in
the conclusion what had been already avowed in the premises.
4°, On this order the objection of petitio princijni stands
hitherto unrefiited, if not unrefutable, against Logic *
5°, In this order the process is complex. The simple thought
is first mentally analysed, if it proceed, as it ought, from the quse-
situm ; but this analysis is not expressed. Then the elements are
recomjiosed, and this recomposition affords the synthetic an-
nouncement of the syllogism, — the syllogism being thus the super-
fluous regress of a foregone analysis. Aristotle's analytic is thus
truly a synthetic ; it overtly reconstructs the elements which had
been attained by a covert analysis.^
6°, In this method, the problem hanging loose from the syllo-
gism, and, in fact, being usually neglected, it does not determine
in the Second and Third Figures one of the two alternative con-
clusions, which, ex facie syllogismi, are competent in them. The
premises only being, there is no reason why one of the conclu-
sions should be drawn to the preference of the other. Mem.
Counter-practice old and new. The logicians ought not, however,
to have ignored this double conclusion,
7°, See corresponding number.
8°, See corresponding number.7
(h) OEDEE OF PEEMISES.
Aristotle places the middle term in the first Figure between the
extremes, and the major extreme first ; — in the second Figure before
the extremes, and the major extreme next to it; — in the third
Figure, after the extremes, and the minor extreme next to it.
a [Stewart (JS'/e)tte>!ts, vol. ii. cb. 3, § 2, commeucing with the letters, Theinean-
Works,Yo\. iii., p. 202, et alibi) makes ing of the term is the doctrine showing
this objection. Refuted by GaUuppi how to analyse or reduce reasonings to
Lez. di Locjica e di Metafisica, Lez. i, p. syllogisms ; syllogisms to figure ; figure
2i2, et seq.'\ to mood; second and third figures to
;8 [Aristotle's Analytics are in syn- first; syllogisms to propositions and
thetic order ; they proceed from the terms ; propositions to terms ; for of all
simple to the compound ; the elements these analysis is said. See Pacii Or-
they commence with are gained by a ganon, An. Prior., i. cc. 2, 32, 42, 44,
foregone analysis, which is not expressed. 45, pp. 128, 261, 273, 275, 278, 280.]
They are as synthetic as a grammar 7 Compare Discussions, p. 652. — Ed.
VOL. II. 2
402 APPENDIX.
In his mode of eiiouncement this rehxtive order is naturally
kept ; for he expresses the predicate first and the subject last,
thus : A is in all B, or A is j^i'edicated of all B, instead of
saying AllJi is A.
But when logicians came to enounce propositions and syllogisms
in conformity to common language, the subject being usually first,
they had one or other of two difficulties to encounter, and submit
they must to either ; for they must either displace the middle term
from its intermediate position in the first Figure, to say nothing
of reversing its order in the second and third ; or, if they kept it
in an intermediate position in the first Figure, (in the second and
third the Aristotelic order could not be kept), it behoved them to
enounce the minor premise first.
And this alternative actually determined two opposite procedures,
— a difference which, though generally distinguishing the logicians
of different ages and countries into two great classes, has been
wholly overlooked. All, it must be borne in mind, regard the
syllogism in Figure exclusively, and as figured only in Extension.
The former difficulty and its avoidance determined the older
order of enouncement, that is, constrained logicians to state the
minor premise first in the first Figure ; and, to avoid the discre-
pancy, they of course did the same for uniformity in the second
and third. Such is the order.
The latter difficulty and its avoidance determined the more
modern order of enouncement, that is, constrained logicians to
surrender the position of the middle term as middle, in following
the order of the major premise first in all the Figures.
Philoponus on the First Book of the Prior Analytics, c. iv. § 4,
(Pacian Division), f. xx. ed. Trincavelh. — " This definition ap-
pears to be of the extremes and of the middle term ; but is not.
It behoves, in addition, to interpolate in tliought an ' only ;' and
thus will it be rightly enounced, as if he had said •, — But the ex-
tremes are both that which is only in another, and that in which
another only is. For if A is [predicated] of all B, and B is [pre-
dicated] of all C, it is necessary that A should be predicated of all
C. This is the first syllogistic mood. Two universal affirmatives,
inferring an universal conclusion. For if B is in all C, conse-
quently C is a part of B; but again B is a part of A ; consequently.
APPENDIX.
403
A is in all C, inasmuch as C is a part of B. But what is here
said will appear more clearly from a concrete example — Sub-
stance of all animal ; animal of all man ; (there follows), sub-
stance of all man. And backwards, [avaTrakiv), All inan ani-
mal ; all animal substance; all 7nan therefore substance. In
regard to this figure, it is plain how we ought to take the terms
of the first mood. The first [major] is most generic ; the second
[middle] is a subaltern genus ; and the third [minor] is a species
more sjjecial than the middle. But a conclusion is here always
necessary. Thus, following the synthetic order, that is, if we start
from the major term, substance begins, beginning also the con-
clusion. Substance of all animal, (substance stands first) ; animal
of all man ; (finally the conclusion commences with substance), —
substance of all inian. But if [on the analytic order] we depart
from the minor term, as from man, in this case the conclusion
will, in like manner, begin therewith: All man animal; all
animal substance ; all man substance. "
This is the only philosophic view of the matter. His syllogisms
really analytic ( = in Depth.)
Analytic and Synthetic ambiguous. Better, — order of Breadth
and Depth."-
a [Instances and authorities for the
enouncement of Syllogism, with the
Minor Premise stated first : —
Ancients.
Greels : — Gregory of Nyssa, Opera, t.
ii. p. 612, in his 12 (not 10) Syllogisms
against Manicheans, varies. These very
coiTupt. Joannes Damascenus, Dialec-
iica, c. 64, Opera ed. Lequien, Paris,
1712, t. i. pp. 65, 66), gives two Syllo-
gisms, one with minor first. Alcinous,
De Doct. Plat. L. i. cc. 5 and 6. Aris-
totle often places minor first. See Za-
barella. Opera Logica, De Qicarta Fiyura,
p. 121. Vallius, Logica, t. ii., pp. 72, 76.
Aristotle and Alexander not regular in
stating major propositions. See in
First Figure, An. Pr. i. c. 4. Aristotle
used the " whole" only of the predicate.
See Zabarella, Tahidce, In An. Prior., p.
149. (But see above, p. 301.) Boethius,
Oyjera, pp. 562, 583. Aristotle, An. Pr.
i. c. 1, suh fine, ubi Alexander, f. 9 a.
Philoponus, f. 17 a. f . 11 b. Alexander
Aph. In An Pr. i. ff. 9 a, 15 b. Philo-
ponus, In An. Pr. i. ff. 11 b, 20 a.
explains the practice of Gieek Peripa-
tetics in this matter. See also ff 17 a,
18 a; and 11 a, 21 a — these in i. Fig. —
in ii. Fig. 23 b. The same In Phy.sica,
i. c. 1, f. 2. Themistius, In An. Post.
ii. c. 4. Anonymiis, De Syllogismo, f.
43 a. Gregorius Aneponymus, Com-
pend. Philosophi(e Syntagma. L. v. cc.
1, 6, pp. 58, 70. Georgius Diaconus
Pachymerius, Epit.Log. tit. iv. cc. 1 — 4.
Sextus Empiricus, Pyn'h. Hypotypos.,
L. ii. cc. 13, 14, pp. 103, 110. Clemens
Alex. Stroyn. L. viii. Opera, p. 784, (ed.
Sylburgii.) Blemmidas, Epitome Logica,
c. 31, p. 219. Gregorius Trapezun-
tius, Dialectica, De Syll. p. 30. " Prima
(Figura) est in qua medius terminus
subjicitur in majore, et in minore
prfcdicatur: quamvis contra fieri et soleat
404
AITENDTX,
R FIGURE— rXFIGUKED AXP FIGURED SYLLOGISM.
(1S5S) (a) Contrast axd Compakijon or tue taeious
KI>vDS OP FOK^LAi SYLLOOI^M — DrFFEKEXCE OF
FlOrRE AOCIDE^~TAL.
A). Unjjgured SifUogi.sm — One form of syllogism : for here there
is abdislied, 1^, The difference of Breadth and Depth, for the t^rms
rf pnmtS" A Greek, he -wrote in Italv
for tike Latins; but refers here to the
practioe of his conntrrmen.
Latism : — CSeero, 2>f Finu ia. 8 ; iv. IS.
TWc, J)M!?T-iii. 7 ; T. 15, Opera Phil, pp.
SS5, S>OS, dSl, 1029, edTerbtn^ Mac-
rolmis, Opera-, p. ISl, ZeuniL Seneca,
E^-nst S5, p S6S. Apuleius, 3c MahiL
jDoct Plat Li. iii. p. S5, ed. Elmenhorst.
Isidciirus, in GotJiqfr. Aurt<>rcs, p. S7S.
Casaodorus, jyiahciica, Oftovi.^ p. 556,
Grenev. 1650, gires altrOTiaiiTe, but in
Psalm •yvri.T. 16, gi"res a svDogisin ■wTth
minor first. Mardanxis Capella, Ik Sfp-
tem Artihug Zibcralibn-R, aHows both
forms for first Figure ; geaierallT makes
the minor first (see below, p. -424), Boe-
thius, (origo maliV t. 0}'i€ra, p. 5^ d
OSIEKIALS.
IS ' - : — ^Axerrc^es (enouncing
as TTr _ . : __ t Jigares, has minor firsx.
(See below, p. 425. 1
JetD^: — Eabbi Simeon [tnilT Maimon-
id«] (in Hebrew.) Loffiaa, per S. Mnn-
stem TD ec. 6, 7, Basil, 1527-
Modem antieipatioiis of iie doctrine
ihai the Minor Premisse shoxild precede
the Major. YaHa, DiaJ^ectica, i. 60 b, &.c.
Opera p. 7§3, 7S6. Joanna Xeomagus,
In TrapezuniiuTn, i S8 b. (only adduce
examples.) Caramuel, Bat. et Mealu Phi-
loBopMa, Loaica. Disp. ix. XTi Aquinas,
OpiiiT. 47. ^Camerarius. Difp. Phil, P. L
qu. IS, p. 117. > Alstedius, EihOfclopa-
rfwjp. 4i7. Ga^endi, Oj>era, iL p. 413 ;
L p. 107. Cameraiins, Disp. PML P. L
qu. IS, p. 117. Leibnita, Opera ix Pais.
i. p. S56. iKsscrf. de Arte Comhimahtria,
(1666^, ed Dutens, who refeis to Ramus,
Gassendi, Alcinous, &c Cf. ^Tonrcayjr
Essais, L ir, § S, p. 454, ed. Raspe : and
Locke's Egnay, ibid. Buffier. Zx^i-ptf,
§ 6S. Csisaiius, Dijil^ti^a. Tract, t. Ik
S^IL Cat p. 15S, vfiis^ e^- 15-5-^- J- C.E.
Xoira iMt'CcM Vcrita-f. kc, see Reusoh,
5 7 ; " " '26. Chau-
v: , r. Figvra.
Hobt'es, L-.'.^ -'J.',,, 0, IT. prefix^ the
minor, I'see HaBam, Lit of Enropf^ vol.
iii c- f ■ ed. lS-3?.^ -
Xcucs "- 36, § 225. 1
Lopl; §
pp. 202, 223. ii^.1
$ 454. Esser, Lo^tJr, § 107, p-
•;: ■: _ ; 5 114, p 40S. Beneke,
.> J .. c T. p. 210 (i iteq.
Stapuiensis, in Sergeant's J/fMod to
S'iencf, p, 127. F:i::::'lati, vthough he
eiTS himseh' } i Lc-pi'dT, p. S65
P. iil c. S, :: - : ^ ^ -_ r re Boethius, Sex-
T 115 Emj'iricTiSs Aieinous, &c, Ch. Mayne
is-sjz 0% ^S'atiiraJ A'i'»riti»^, p 122 ff «■?.
Lamy, Acta Eru'^„ 170S, p. 67.
"VTho haxe erred in this subject. —
making our ordo- of enuiMsataon the
natural and ii": n" VVes, Cemfvra Vert.
Opera, %. i. " . G. Tossius. Be
yai. Art. 1,-. u... L.,i^yi, c viiL § 9.
J. A. Fabridus, Ad. Sext. Em p. 103.
Faeciolati, iT ' "
Waitz, Ir, (■
That Rf.- -
Qtantrty n. - "
Mai^ § 3?&, p. c.:. :.
Logicum, § 5i7. Schul;.
old, aS17) § 72 of last
■ - 7. S6.
. :_: rr_cnsiTe
Wolf, PJiil.
,1. ^ . !^ema
. ; 77 of
^i•-; edition.
ars ^I'tJ: ^~'*"'^'
AFPES338K.
4m
-iSfi irx!--
-X levTi-
""fflasiasi
tjSI iSir Jffli^IH3Ci&
im nf ■?.(/7.it iirrici, jgrTiHrr^ smn— Zrcinini
jf im iLioiJE'i if HJiuiujnc.. 1.. Ijit.. Zx j?araF-
TaoLsi. -ZaS: WmTr- Zl^l+IIIIHfc. llff ^ ;= Sb
SSiCTr SS^St 'al& '""ftrnTfriwHrnT icSE. {Iff JL =
H. jrar A = M. 'aw£ JE = JS .. nr iai.^ :ffis
406 APPENDIX.
If rule true, it will follow that it is of no consequence whether : —
]°, The middle one or any other of the three terms be, in any
proposition, subject or predicate, if only either. Hence difference
of Figure of no account in varying the syllogism. Thus, (retain-
ing the subordination of terms), convert major proposition in Ex-
tension of first Figure, and you have second Figure ; convert
minor proposition, and you have third Figure ; convert both pre-
mises, and you have fourth Figure.
2°, Whether one of the extremes, one or other of the premises,
stand first or second, be, in fact, major or minor term of a propo-
sition ; all that is required is, that the terms and their quantities
should remain the same, and that they should always bear to each
other a relation of subject and predicate. Thus, if [in] any of the
Figures, the major and minor terms and projiositions interchange
relation of subordination ; when, in the first Figure, you convert
and transpose ; and when [in] the other three Figures (fourth ?),
you simply transpose the premises.
Indifferent (in first Figure) which premise precedes or follows.
For of two one not before the other in nature. But not indiffer-
ent in either whole, which term should be subject and predicate
of conclusion.*
(b) Double Conclusion in Second and Thied Figures.
My doctrine is as follows : —
In the Unfigured Syllogisin there is no contrast of terms, the
notions comjiared not being to each other subject and predicate ;
consequently, the conclusion is here necessarily one and only one.
In the Figured Syllogisin we must discriminate the Figures.
In the First Figure, where the middle term is subject of the one
extreme and predicate of the other, there is of course a determinate
major extreme and premise, and a determinate minor extreme and
premise ; consequently, also, one proximate or direct, and one remote
or indirect, conclusion, — the latter by a conversion of the former.
« Compare Discussions, p. 6o3. — Ed.
APPENDIX. 407
In the Second and Third figures all this is reversed. In these
there is no major and minor extreme and premise, both extremes
being either subjects or predicates of the middle ; consequently,
in the inference, as either extreme may be indifferently subject or
predicate of the other, there are two indifferent conclusions, that
is, conclusions neither of which is more direct or indirect than the
other.
This doctrine is opposed to that of Aristotle and the logicians,
who recognise in the Second and Third Figures a major and minor
extreme and premise, with one determinate conclusion.
The whole question in regard to the duplicity or simplicity of
the conclusion in the latter figures depends upon the distinction
in them of a major and a minor term ; and it must be peremp-
torily decided in opposition to the universal doctrine, unless it can
be shown that, in these figures, this distinction actually subsists.
This was felt by the logicians ; accordingly they applied themselves
with zeal to establish this distinction. But it would apjDcar, from
tlie very multiplicity of their opinions, that none jiroved satisfac-
tory ; and this general presumption is shown to be correct by the
examination of these opinions in detail, — an examination which
evinces that of these opinions there is no one which ought to
satisfy an inquiring mind.
In all, there are six or five different grounds on wdiich it has
been attempted to establish the discrimination of a major and
minor term in the Second and Third Figures. All are mutually
subversive ; each is incompetent. Each following the first is in
fact a virtual acknowledgment that the reason on which Aristotle
proceeded in this establishment, is at once ambiguous and insuffi-
cient. I shall enumerate these opinions as nearly as possible in
chronological order.
1. That the major is the extreme which lies in the Second
Figure nearer to, in the Third Figure farther from., the middle. —
This is Aristotle's definition, {An. Pr., L. i., cc. 5, 6). At best it
is ambiguous, and has, accordingly, been taken in different senses
by following logicians ; and in treating of them it will be seen
that in none, except an arbitrary sense, can the one extreme, in
these figures, be considered to lie nearer to the middle term than
the other. I exclude the supposition that Aristotle spoke in
reference to some scheme of mechanical notation.
408 APPENDIX.
2. That the major term in the antecedent is that ivhich is pre-
dicate ill the conclusion. — This doctrine dates from a remote an-
tiquity. It is rejected by Alexander; bnt, adopted by Ammonius
and Philoponus, (f. 17 b, 18 a., ed. Trine), has been generally
recognised by subsequent logicians. Its recognition is now almost
universal. Yet, critically considered, it explains nothing. Educing
the law out of the fact, and not deducing the fact from the law, it
does not even attempt to show why one being, either extreme may
not be, predicate of the conclusion. It is merely an empirical, —
merely an arbitrary, assertion. The Aphrodisian, after refuting
the doctrine, when the terms are indefinite (preindesignate), justly
says : — " Nor is the case different when the terms are definite
[predesignate]. For the conclusion shows as predicate the term
given as major in the premises ; so that the conclusion is not itself
demonstrative of the major ; on the contrary, the being taken in
the premises as major, is the cause why a term is also taken as
l^redicate in the conclusion." — [An. Pr. £ 24 a, ed. Aid.)
3. That the proximity of an extreme to the middle term, in
Logic, is to be decided hy the relative p)roxiniity in nature, to the
7niddle notion of the notions compared. This, which is the inter-
pretation of Aristotle by Herminus, is one of the oldest upon re-
cord, being detailed and refuted at great length by the Aphrodi-
sian, (f 23 b, 2-i a). To determine the natural proximity re-
quired is often difficult in affirmative, and always impossible in
negative, syllogism ; and, besides the objections of Alexander, it is
wholly material and extralogical. It is needless to dwell on this
opinion, which, obscure in itself, seems altogether unknown to our
modern logicians.
4. That the major term in the Syllogism is the p)redicate of
the problem or question. This is the doctrine maintained by
Alexander, (f 24 b) ; but it is doubtful whether at first or second
hand. It has been adopted l^y Averroes. Zabarella, and sundry of
the acuter logicians in modern times. It is incompetent, however,
to establish the discrimination. Material, it presupposes an inten-
tion of the reasoner ; does not appear e^/ac?'e syllogismi; and, at
best, only shows Avhich of two possible qu^esita, — which of two
possible conclusions, — has been actually carried out. For it as-
sumes, that of the two extremes either might have been major in
the antecedent, and predicate in the conclusion. If Alexander
APPENDIX. 409
had applied the same subtlety in canvassing his own opinion,
which he did in criticising those of others, he would not have
given the authority of his name to so untenable doctrine.
5. That the major extreme is that contained in the major jwe-
mise, and the major premise that in the order of enouncement
first. This doctrine seems indicated by Scotus, (An. Pr., L. i.,
qu. xxiv. §§ 5, 6) ; and is held explicitly by certain of his fol-
lowers. This also is wholly incompetent. For the order of
the premises, as the subtle Doctor himself observes, {Ih., qu.
xxiii. § 6), is altogether indifferent to the validity of the con-
sequence ; and if this external accident be admitted, we should
have Greek majors and minors turned, presto, into Latin minors
and majors.
6. That the major extreme is that contained in the major pre-
mise, and the major premise that itself most general. All oppo-
site practice originates in abuse. This opinion, which coincides
with that of Herminus, (No. 3), in making the logical relation of
terms dependent on the natural relation of notions, I find ad-
vanced in 1614, in the Disjmtationes of an ingenious and inde-
pendent philosopher, the Spanish Jesuit, Petrus Hurtado de Men-
doza, {Disp.Log. et Met., I., Disp. x. §§ 50 — 55). It is, however,
too singular, and manifestly too untenable, to require refutation.
As material, it is illogical ; as formal, if allowed, it would at best
serve only for the discrimination of certain moods ; but it cannot
be allowed, for it would only subvert the old without being ade-
quate to the establishment of aught new. It shows, however, how
unsatisfactory were the previous theories, when such a doctrine
could be proposed by so acute a reasoner, in substitution. This
opinion has remained unnoticed by posterior logicians.
The dominant result from this historical enumeration is, that,
in the Second and Third Figures, there is no major or minor term,
therefore no major or minor premise, therefore two indifferent
conclusions.
This important truth, however natural and even manifest it may
seem when fully developed, has but few and obscure vaticinations
of its recognition during the progress of the science. Three only
have I met with.
The first I find in the Aphrodisian, (f 24 b) ; for his expres-
sions might seem to indicate that the opinion of there being no
410 APPENDIX.
major and minor term in the second figure, (nor, by analogy, in the
third), was a doctrine actually held by some early Greek logicians.
It would be curious to know if these were the " ancients," assailed
by Ammonius, for maintaining an overt quantification of the pre-
dicate. The words of Alexander are : — " Nor, however, can it be
said, that in the present figure there is no major. For this at least
is determinate, — that its major must be universal ; and, if there be
in it any syllogistic combination, that premise is the major, which
contains the major term ; " (f 24 a.) Demurring to this refuta-
tion, it is, however, evidence sufficient of the opinion to which it
is opposed. This, as it is the oldest, is, indeed, the only authority
for any deliberate doctrine on the point.
The second indication dates from the middle of the fifteenth
century, and is contained in the Dialectica of the celebrated Lau-
rentius Valla (L. iiL c. 8 [51]). Valla abolishes the third figure, and
his opinion on the question is limited to his observations on the
second. In treating of Cesare and Camestres, which, after a host
of previous logicians, he considers to be a single mood ; there is
nothing remarkable in his statement : " Neque distinctre sunt pro-
positio et assumptio, ut altera major sit, altera minor, sed quodam-
modo pares ; ideoque sicut neutra vindicat sibi primum aut secun-
dum locum, ita utraque jus habet in utraque conclusione. Verum
istis placuit, ut id quod secundo loco poneretur, vendicaret sibi con-
clusionem : quod verum esset nisi semper gemina esset conclusio.
Sed earum dicamus alteram ad id quod primo loco, alteram ad id
quod secundo loco positum est referri" We, therefore, await the
development of his doctrine by relation to the other moods, Festino
and Baroco, which thus auspiciously begins : — " Idem contingit in
reliquis duobus : qui tamen sunt magis distincti." We are, how-
ever, condemned to disappointment. For, by a common error,
excusable enough in this impetuous writer, he has confounded sin-
gulars (definites) with particulars (indefinites) ; and thus the ex-
amples which he adduces of these moods are, in fact, only examples
of Cesare and Camestres. The same error had also been previ-
ously committed (L. iii. c. 4.) The whole, therefore, of Valla's
doctrine, which is exclusively founded on these examples, must go
for nothing ; for we cannot presume, on such a ground, that he
admits more than the four common moods, identifying, indeed, the
two first, by admitting in them of a double conclusion. We can-
APPENDIX, 411
not, certainly, infer, that he ever thought of recognising a par-
ticular, — an indefinite, predicate in a negative proposition.
The third and last indication which I can adduce is that from
the Method to Science of John Sergeant, who has, in this, as
in his other books, (too successfully), concealed his name under
the initials " J. S." He was a Catholic priest, and, from 1665, an
active religious controversialist : whilst, as a philosopher, in his
Idea Philosophice Gartesianw, a criticism of Descartes, in his
Solid Pliilosophy, a criticism of Locke," in his Metaphysics, and in
the present work, he manifests remarkable eloquence, ingenuity,
and independence, mingled, no doubt, with many untenable, not to
say ridiculous, jiaradoxes. His works, however, contain genius
more than enough to have saved them, in any other country, from
the total oblivion into which they have fallen in this, — where, in-
deed, they probably never were appreciated. His Method to Sci-
ence, (a treatise on Logic), was published in 1696, with a "Preface,
dedicatory to the learned students of both our Universities," ex-
tending to sixty-two pages. But, alas ! neither this nor any other
of his philosophical books is to be found in the Bodleian.
In the third book of his Method, which treats of Discourse,
after speaking of the first, or, as he calls it, " only right figure of a
syllogism," Ave have the following observations on the second and
third : — " § 1 4. Wherefore the other two figures, [he does not recog-
nise the fourth], are imnatural and monstrous. For, since nature
has shown us, that what conjoins two notions ought to be placed
in the middle between them ; it is against nature and reason to
place it either above them both, as is done in that they call the
second figure, or under them both, as is done in that figure they
call the third.
" § 15. Hence no determinate conclusion can follow, in either of
the last figures, from the disposal of the parts in the syllogisms.
For since, as appears, (§ 13), the extreme which is predicated of
the middle term in the major, has thence a title to be the predi-
cate in the conclusion, because it is above the middle term, which
is the predicate, or above the other extreme in the minor, it fol-
« Sergeant is an intelligent antagonist certain views he anticipates Kant ; and
of both these philosophers, and I have Pope has evidently taken from his bro-
else where had occasion to quote hina as ther Catholic the hint of some of his
the first and one of the ablest critics of most celebrated thoughts.
the Essay on Human Understanding. In
412 APPENDIX.
lows, that if the middle term be twice above or twice heloiu the
other two terms in the premises, that reason ceases ; and so it is
left indifferent which of the other terms is to be subject or predi-
cate in the conclusion ; and the indeterminate conclusion follows,
not from the artificial yb?"m of the syllogism, but merely from the
material identity of all the three terms ; or from this, that their
notions are found in the same Ens. Wherefore, from these pre-
mises, [in the second figure],
Some laudable thing is [all] virtue,
[All] courtesi/ is a virtue ;
or, from these, [in the third],
[All] virtue is [somel laudable,
Some virtue is [all] courtesy ;
the conclusion might either be,
Therefore, [all] courtesy is [some] laudable.
Or, So7ne laudable thing is [all] courtesi/.
So that, to argue on that fashion, or to make use of tliese awk-
ward figures, is not to know certainly the end or conclusion we
aim at, but to shoot our bolt at no determinate mark, since no
determinate conclusion can in that case follow." (P. 232).
Extremes, it is said, meet. Sergeant would abolish the second
and third figures, as petitory and unnatural, as merely material
corruptions of the one formal first. I, on the contrary, regard all
the figures as equally necessary, natural, and formal. But we
agree in this : both hold that, in the second and third figures, there
is a twofold and indifferent conclusion ; howbeit, the one makes
this a monstrosity of the syllogistic matter, the other, a beauty of
the syllogistic form. Therefore, though I view Sergeant as wrong
in his premises, and " shooting his bolt at no determinate mark,"
I must needs allow that he has, by chance, hit the bull's eye. I
have inserted, within square brackets, the quantifications required
to restore and show out the formality of his examples ; on my
scheme of notation, they stand as follows : —
r
APPENDIX. 413
C— HISTORICAL NOTICES REGARDING FIGURE OF
SYLLOGISM.
I. — Aristotle.
Aristotle ; Figures and Terms of Syllogism, Prior Analytics
B. I. ch. iv.
First Figure, ch. iv. — § 2. " When three terms [or notions] hold
this mutual relation, — that the last is in the whole middle, whilst
the middle is or is not in the whole first, — of these extremes
there results of necessity a perfect syllogism.*
§ 8. " By middle term, [B (B)], I mean that which itself is in
another and another in it ; and which in position also stands in-
termediate. I call extreme both that which is itself in another
[the minor], and that in which another is [the major]. For if A
be predicated of all B, and B of all C, A will necessarily be pre-
dicated of all C.
§ 10. "I call that the major extreme [A (A)] in which the
middle is; the minor [r (C)] that which lies under the middle."
Second Figure, ch. v. — § 1. " When the same [predicate notion]
inheres in all of the one and in none of the other, or in all or in
none of both [the subject notions], — this I denominate the Second
Figure.
§ 2. " The 7niddle [M (M)] in this figure I call that which is
predicated of both [notions] ; the extremes, the [notions] of which
the middle is said. The major extreme [N (N)] is that towards
a Ch. iv. § 2. — This definition of the the higher notion A : and with reference
First Figure, (founded on the rules De to comprehension, — for the higher no-
Omni and de Nullo), ai:)plies only to the tiou A as contained in the all or whole
universal moods, but, of these, onlj' to of the lower notion B. In the former
those legitimate and useful, — Barbara sense, which with Ai-istotle is the more
and Celarent. It, therefore, seems in- usual, and, in fact, the only one con-
adequate, but not superfluous. templated by the logicians, there is also
Aristotle uses the phrase " to be in to be observed a distinction between
all or in the wJiole," both with reference the inhesion and the predication of the
to extension, — for the lower notion B, attribute,
as contained under the all or whole of
414
APPENDIX.
the middle ; the minor [3 (0)], that from the middle more
remote.
§ 3. " The middle is placed out [from between] the extremes,
the first in position" —
[So, M
N
M
■N
Third Figm-e, eh. vi. — § 1. "Wlien in the same [subject notion]
one [predicate notion] inheres in all, another in none of it, or
when both inhere in all or in none of it, such figure I call the
Third.
§ 2. " In this [figure] I name the middle, that of which both
[the other terms] are predicated ; the extremes, the predicates
themselves. The major extreme [n (P)] is that farther from, the
minor [P, (Q)], that nearer to, the middle.
§ 3. " The middle [^ (R)] is placed out [from between] the
extremes, the last in position,"
[As, n
p
2
Aristotle, Prior Ancdytics, B. i. c. 23, § 7.
General Theory of Figure. — " If, then, it be necessary [in reason-
ing] to take some [term] common [or intermediate] to both [ex-
treme terms] ; this is possible in three ways. For we predicate
either [the extreme] A of [the middle] C, and [the middle] C of
[the extreme] B ; or [the middle] C of both [extremes] ; or both
[extremes] of [the middle] 0. These are the [three] Figures of
which we have spoken ; and it is manifest, that through one or
other of the Figures every syllogism must be realised.""
a Aristotle here varies the notation tion might appear to indicate), that the
liy lettex's of the three syllogistic terms middle term was a notion in the First
making C (r) stand for the middle Figure, necessarily intermediate be-
term, A and B for the two extremes, tween the two extremes, in the Se-
This he did, perhaps, to prevent it be- cond superior, in the Third inferior, to
ing supposed, (what his previous nota- them.
APPEIfDIX. 415
II. AND III. — AlEXANDEE AND HeEMINUS.
Alexander, In An. Pr.^ f. 23 b.
Second Figure, c. v. Aristotle. — " ' The middle extreme is that
which lies towards the middle.'
§ 2. " But it is a question, whether in the Second Figure there
be by nature any major and minor extreme, and if there be, by
\vhat criterion it may be known. For if we can indifferently con-
nect with the middle term whichsoever extreme we choose, this
we may always call the major. And as negative conclusions only
are drawn in this figure, universal negatives being also mutu-
ally convertible, it follows, that in universal negatives the one
term has no better title to be styled major than the other, seeing
that the major term is what is predicated, whilst both are here
indifferently predicable of each other. In universal affirmatives,
indeed, the predicate is major, because it has a wider extent ; and
for this reason, such propositions are not [simply] convertible ;
so that here there is by nature a major term which is not to be
found in universal negatives.
" Herminus is of opinion that, in the Second Figure,
[1°.] "If both the extremes, of which the middle is predicated,
be homogeneous [or of the same genus], the major term is that most
proximate to the genus common to the two. For example : —
If the extremes be bird and man ; hird lying nearer to the com-
mon genus [cinimal] than man, as in its first division, hird is
thus the major extreme ; and, in general, of homogeneous terms,
that holding such a relation to the common genus is the major.
[2°.] "But if the terms be equally distant from the common genus,
as horse and man, we ought to regard the middle predicated of
of them, and consider of which [term] it is predicated through
[that term] itself, and of which through some other predicate ;
and compare that through which it is predicated of another with
that through which it is predicated of [the term] itself. And if
that through which [the middle] is predicated of another, (viz.
the one extreme), be nearer [than the other extreme] to the
common genus, that [extreme] of which [for rovTOiv ov, I read
TovTov ov\ the middle is [mediately] predicated, from its closer
propinquity to the common genus, rightly obtains the title of
major. For example : If the extremes be horse and man,
416 ArPENDIX.
rational being predicated of them, — negatively of horse, affirma-
tively of man ; seeing that rational is not of itself denied of
horse, but because horse is irrational, whereas 7'ational is of
itself affirmed of man, horse is nearer than man to their common
genus animal ; horse will, therefore, be the major extreme, though
man be no further removed than horse from its proper genus.
And this, because that through which the predicate [i.e. the middle]
is predicated of this last, as being irrational, is greater ; for ra-
tional is not denied of horse qua horse, whilst it is affirmed of
onan qua man.
[3°.] " But if the extremes be not homogeneous, but under ditfe-
rent genera, that is to be considered the major term, which of the
two holds the nearer of its own genus. For instance : If aught be
predicated of colour and man, colour is the major extreme ; for
colour stands closer to q ual it i/, tlmn man to substance: as man
is an individual [or most special] species, but not colour.
[4°.] "Finally, if each be equally remote from its proper genus,
we must consider the middle, and inquire of which term it is pre-
dicated through [that term] itself, and of which through some-
thing else ; and if that, through which the middle is predicated
of another, [i.e. one extreme], be nearer to its proper genus, and if
through that the middle be actually predicated of this term, this
term is to be deemed the major. For example : If the terms be
white and man, the one being an individual species in quality, the
other in substance ; and if rational be affirmatively predicated of
man, negatively of white ; the affirmation is made in regard
to man as mcin, whereas the negation is made of white, not as
wJiite, but as inanimate. But since inanimate, through which
rational is denied of white, is more common, more universal, and
more proximate to substance inanimate than man to [suhstance'\
animate, on that account, white is the major term in preference to
man!' [So far Herminus.]
" But to reason thus, and to endeavour to demonstrate a major
term by nature, in the Second Figure, is a speculation which may
be curious, but is not true. [I read Trpog tw.]
[1°]. " For, in the first place, if we consider the given terms,
not in themselves, but in relation to others, in which the predi-
cated term does not inhere ; the major term will be always found
in the negative proposition. For, in this case, the major is always
APPENDIX. 417
equal to the middle terra ; since whether it be thus or thus taken
from the commencement, or be so made by him who denies it, the
negative major will still stand in this relation to the middle term.
For the middle does not inhere, where it is not suj)posed to inhere.
Wherefore, its repugnant opposite inheres in the subject, but the
repugnant opposite of the middle is equal to the middle. And
this, either through the middle itself, or through another notion of
wider extent ; as when rational is denied of something through
inanimate. For there is here an equalisation through irrational,
through which rational is negatively predicated of horse. For
either the middle is equal to this of which it is denied, or [I read,
Ty for 6] it is less ; as when, through inanimate, rational is de-
nied of aught. For inanimate is equal to animate, under which
is rational, a notion greater than that other of which it is affirmed.
For since the affirmative predicate is greater than its subject, of
which the middle is denied or not affirmed ; and since the reason
why the middle is denied, is equal to or greater than the middle
itself, which middle, again, in an affirmative proposition, is greater
than its subject ; — on these accounts, a negative proposition is
always greater than an affirmative. Nevertheless, Aristotle him-
self says that a negation is to be placed in the minor [proposi-
tion] ; for the second syllogism in this figure [Camestres] has as
its minor premise an universal negative.
[2°]. " Further, why in the case of negatives alone should explan-
ation or inquiry be competent, in regard to the reason of the nega-
tive predication, seeing that in the case of affirmatives the reason
is equally an object of inquiry? For rational is predicated of
man, of itself, indeed, but not primarily, that is, not inasmuch as
he is man, but inasmuch as he is rational; so that if rational
[be denied] of Jiorse through iri^ational, still these are both
branches of the same division. By this method, assuredly, no
major can be ever found. Wherefore, we ought not, in this way,
to attempt a discrimination of the major of affirmative syllogisms
in the Second Figure. For in this figure affirmation and negation
are equally compatible with the major term ; so that whatsoever
term has by the forementioned method been found major, the same,
taken either as major or minor, will efiectuate a syllogistic juga-
tion ; which being competent, there is no longer any major [or
minor] in this figure. For the problem is to find not a major
VOL. II. 2 D
418 APPENDIX.
term absolutely, but one of this figure." [So much touching Her-
minus.]
[3°]. " Nor, on the other hand, as is thought by some, is that un-
conditionally to be called the major term, which stands predicate
in the conclusion. For neither is this manifest ; if left indefinite
[preindesignate], the same term will hold a different relation,
thouo;li a conversion of the universal neo;ative ; so that what is
now the major, may be anon the minor ; we may, in fact, be said to
constitute the same term both major and minor. Naturally there
is in negative propositions no major notion, nor, from the conclu-
sion, ought we to make out the major at all. Nor is the case
different when the term is defined [predesignate]. For the con-
clusion shows, as predicate, the term given as major in the pre-
mises ; so that the conclusion is not itself demonstrative of the
major ; on the contrary, the being taken in the premises as
major is the cause why a term is also taken as predicate in the
conclusion.
" Nor, however, can it be said that in this figure there is no major.
For this at least is determinate, — that its major must be universal;
and, if there be [in it] any syllogistic combination, that premise is
the major which contains the major term.
[4°] " But, in the Second Figure, which of the terms is to be
deemed the major ? That is to be deemed the major, and to be
placed first, which in the problem [question or quresitum] we intend
to demonstrate, and which we regard as predicate. For every one
who reasons, first of all determines with himself, what it is he
would prove ; and to this end he applies his stock of suitable pro-
positions ; for no one stumbles by chance on a conclusion. The
notion, therefore, proposed as predicate in the problem to be
proved, is to be constituted the major term ; for although the pro-
position be converted, and the notion thereby become the subject,
still in what we proposed to prove, it [actually] was, and, there-
fore, [virtually] remains, the predicate. Hence, even if there be
drawn another conclusion, w^e convert it ; so that, to us who prove
and syllogise and order terms, that always stands as the major.
For major and minor are not, in negative syllogisms, regulated by
their own nature, but by the intention [of the reasoner] to con-
clude. Thus it is manifest, that what is the predicate in the pro-
blem, is also the predicate in the conclusion."
APPENDIX. 419
Alexander on Prior Analytics, L. i. c. vi., f. 30 a. ed. Aid.
(Third Figure.) . . . This is the Third Figure, and holds the
last place because nothing universal is inferred in it, and because
sophistical syllogisms chiefly aff'ect this figure with their indefinite
and particular conclusions. But the sophistical are the last of all
syllogisms. . . . Add to this, that while both the Second and
Third Fio;ures take their origin from the First of the two, the
third is engendered of the inferior premise. For the minor, qua
minor, is the inferior premise, and holds reasonably a secondary
place, [the conversion of the minor proposition of the first figure
giving the third figure].
F. 30 b. (Darapti.) " The first syzygy in this figure is of two
universal affirmatives [Darapti.] But it may be asked — Why,
whilst in the second figure there are two syllogistic conjugations,
having one of the premises an universal affirmative, the other an
universal negative, (from having, now their major, now their
minor, as an universal negative proposition converted) ; — why, in
the third figure, there is not, in like manner, two syllogistic com-
binations of two universal affirmatives, since of these, either the
major or the minor proposition is convertible ? Is it that in the
second figure, from the propositions being of diverse form [quality],
the commutation of a universal negative into something else by
conversion is necessary, this being now the major, now the minor,
and it not being in our power to convert which we will ? In the
third figure, on the other hand, there being two universal affirma-
tives, the position [relation] of the propositions, (for they are simi-
lar in character and position), is not the cause of one being now
converted, now another ; the cause lying in us, not in the jugation.
Wherefore, the one or other being similarly convertible, inasmuch
as the position [relation] of the two propositions is the same ; the
one which aff'ords the more important probation is selected, and
hereby is determined the syllogistic jugation. Moreover, tlie dif-
ferences of syllogism [moods] in each figure are eff'ected by the
diff'erences among their jugations, not by those among their proba-
tions. Thus that the combination of propositions is syllogistic [or
valid], is proved by conversion and reductio ad imjwssibile, also by
exposition. But from this circumstance there does not emerge a
plurality of syllogisms [moods]. For the different probations [are
not valid from such plurality, but] from the unity of the jugation
.4
420 APPENDIX.
from which they are inferred, so that one j ligation of two universal
affirmatives may constitute, in the third figure, a single syllogism
[mood], howbeit the probations are different ; inasmuch as now
the one, now the other, of the propositions can be converted."
IV. — Philoponus.
Philoponus (or rather Ammonius) on Aristotle, An. Pr., i. 4,
§ i. f 17 a. ed. Trincavelli, 1536.
" The Predicate is always better than the Subject, because the
predicate is, for the most part, more extensive (cTrt irXeov) than the
subject, and because the subject is analogous to the matter, the
predicate to the form ; for the matter is the subject of the forms.
But when the middle term is predicated of the two extremes, or is
the subject of both ; in this case, it is not properly intermediate.
But, howbeit, though in position external to the middle, it is still
preferable to be the predicate than to be the subject. On this
ground, that is called the first figure, the middle term of which
preserves its legitimate order, being subject of the one extreme,
and predicate of the other. The second figure is that in which the
middle is predicated of both extremes, and in which it occupies
the better position of those remaining. Finally, the third figure
is that in which the middle term is subjected to the two extremes ;
here obtaining only the lowest position. Wherefore, in the first
figure the middle term is delineated on a level with the extremes ;
whereas in the second it is jjlaced above, and in the thkd below,
them."«
Philoponus (or rather Ammonius) on Aristotle, An. Pr., f 17
a, ed. Trincavelli, 15.36.
a Ammonius, or Philoponus, here ma- than Ammonius does not appear ; for
nifestly refers to the diagrams represent- they are probably not the constructions
lug the three figures, and accommodated referred to by Aristotle ; and none are
to Aristotle's three sets of letters, noting given by the Aphrodisian in his original
thethreetermsin each of these; thus:— text, though liberally sui^plied by his
Latin translator. The diagrams of Am-
monius were long generally employed.
By Neomagus 1533 (In Trapezimtii Dia-
lect., f. 35), they are most erroneously
t y referred to Faber Stapulensis. [See
Whether these diagrams ascend higher further, Discussions, p. 670. — Ed.]
APPENDIX. 421
Syllogistic Figures in general. — " We must premise what
is the Major Proposition of the Syllogism, and what the Minor.
But to understand this, we must previously be aware what are
the Major and Minor Terms. And it is possible to define
these, both, in common, as applicable to all the three figures
and, in special, with reference to the first alone. In the latter
relation, that is, regarding si^ecially the first figure, the Major
term is that which constitutes the Predicate, the Minor that
tvhich constitutes the Subject, of the Middle, so far as limited
to the first figure. But since in neither of the other figures do
the extremes reciprocally stand in any definite (?) relation to the
middle term ; it is manifest that this determination is inajDplicable
to them. We must, therefore, employ a rule common to all the
three figures ; to wit, that the major term is that predicated, the
minor that subjected, in the conclusion. Thus, the Major Proposi-
tion is the one containing the Major Term ; the Minor Propo-
sition the one containing the Minor Term. Examples : Of the
First Figure, — Man [t's] animal; animal, substance ; therefore,
man, substance Of the Second, — Animal [is predi-
cated] of all man; animal of no stone; man, therefore, of no
stone. ... Of the Third, — Some stone is white ; all stone
is inanimate ; cansequenthj, some white is inanimate." . . .
First Figure.— F. 19 b. 59 ; Aristotle, I. c. § 3. "'But I call
that the middle term which itself is in another, and another in it ;
and which in position lies intermediate.'
" This definition of the middle term is not common to the three
figures, but limited to the middle of the first figure only. For,
&c But, if there be a certain difference in species
between the middle terms of the three figures, they have likewise
something in common ; to wit, that the middle term is found
twice in the premises, throughout the three figures ; which also in
position is middle. For Aristotle wishes in the Diagraph (iu avrrj
TT) Kara'ypa(f)y) to preserve the order of intermediacy, so that,
placing the three terms in a straight line, we assign the middle
place to the middle term. [?]
Aristotle, I. c. § 4. " ' But [I call] the extremes both that which
is in another, and that in which another is. For if A be predi-
cated of all B, and B of all C, it is necessary that A should also be
422 APPENDIX.
predicated of all C. We have previously said what we mean by
the expression [predicated] of all! "
" It may seem perhaps that this is a [perfect] definition of the
extremes and of the middle term. But it is not ; for it behoves
us to sub-understand, in addition, the word only ; and thus the
definition will rightly run, — But [I call] the extremes, both that
which is in another [minor], and that in which another is [major]
For if A be predicated by all B, and B of all C, it is necessary
that A be predicated of all C.
" This the first syllogistic mood is of two affirmative universals,
collecting an affirmative conclusion. Por if B inhere in all C, C is,
consequently, a part of B. But B is a part of A ; A therefore,
also, inheres in all C, C being a part of B. The reasoning will be
j)lainer in material examples — as substance [is predicated] of all
animal ; animal of all man ; and there is ixdexiedi substance of all
man; and conversely, a/Z 7?icm {in] animal; all animal substance ;
therefore, all man substance.
" But it is manifest how, in this figure, the terms of the first mood
[Barbara] ought to be taken. The first is the most general, and the
second the subaltern, genus ; whilst the third is a species more spe-
cial than the middle. The conclusion ought always to be drawn.
Thus, if, proceeding synthetically, we commence by the major term
[and proposition], substance begins ; wherefore it also leads the
way in the conclusion. [There is predicated] substance of all
animal (here substance commences) ; animal of all man ; whilst
the conclusion again commences with substance, — substance of all
man. But if we start from the minor term [and proposition], as
from man, with this also the conclusion will commence : all man
[is] animal ; all animal substance ; all man substance.
" Aristotle takes the terms A, B, C ; and, from the relation of the
letters, he manifests to us the order of the first figure. The major
terra he calls A, because A stands first in order ; the minor term,
C ; and the middle term B, as B, in its order, follows A, and pre-
cedes C.
" It is plain that the terms may possibly be coadequate [and
therefore reciprocating]; as receptive of science — risible — man;
for all man is 7'isible ; all risible is receptive of science ; therefore,
all man is receptive of science."
APPENDIX. 4j23
F. 23 b, Aristotle ch. 5, § 2, Second Figure. " ' The major ex-
treme is that which lies nearer to the middle ; the minor, that
which lies farther from the middle.'
" In place of more akin and more proximate to the middle ; not
in position, but in dignity. For since, of the terms, the middle is
twice predicated, while, in the conclusion, the major is once pre-
dicated, but the minor not even once predicated ; [consequent-
ly], that which is once predicated will be the more proximate to
that which is twice predicated, that is, to the middle, than that
which is not even once predicated. Wherefore, we shall hear him
[Aristotle], in the Third Figure, calling the minor the term more
proximate to the middle on account of their affinity, for they are
both subjects, while he calls the major term the more remote.
Perhaps, also, he wishes that in the diagraph (rfj KaTaypa^rj),
the major term should be placed closer to the middle, and the
minor farther off. But the major extreme in this figure, the two
premises being universal, exists not by nature but by position, for the
first of the extremes which you meet with as a subject in the second
figure, — this is the minor extreme, the other is the major. So in
the example — All man an animal ; no plant animal ; therefore, no
man plant. In like manner, if we take the commencement from
plant, this becomes the minor term, and man the major ; as no
plant animal ; all man animal ; no plant,therefore,man. Con-
sequently, the major and minor terms exist in these examples, only
by position, not by nature. If, indeed, one or other of the proposi-
tions be particular, the major and the minor terms are then determin-
ed ; for we hold that in this figure the universal is the major."
Aristotle. — § 3. " 'The middle is placed external to, [not between],
the extremes, and first in position.'
" The middle term passes out of what is properly the middle
position ; it is also placed out of or external to the extremes ; but
either above these or below. But if it be placed above, so as to be
predicated of both, it is called first in position ; if below, so as to
be subjected, it is called second. Wherefore, here, as predicate
of both premises, he styles the middle term the first ; for if it
be placed above, it is first in position, and, in being apart from the
extremes, it is placed without them."
Aristotle, ch. 6, § 2. Third Figure, f 27, b. " ' The major ex-
424 APPENDIX.
treme is that more remote from, the minor is that more proximate
to, the middle.'
"The major term in this figure is twice predicated of the middle,
and in the conclusion ; but the minor once only, and that of the
middle, for it is subjected to the major in the conclusion ; the
middle is alone subjected, never predicated. When he, therefore,
says that the major term is more remote from the middle, he means
the term always predicate is in affinity more remote from that
which is never predicate, but always subject. And that which is
never subject is the major and more proximate term ; that again,
which is now subject, now predicate, is the minor."
V. — MAETIANUS CAPELLA.a
Martianus Capella, De Septem Artihus Liber alihus, L. iv. De
Dialectica, in capite, Quid sit Predicativus Syllogismus, p. 127,
ed Grotii ; p. 83, ed Basil. 1582.
" Hujus generis tres formae [figurse] sunt.
" Prima est, in qua declarativa [prgedicatum] particula superioris
sumpti, sequentis efficitur subjectiva [subjectum] ; aut subjectiva
superioris, declarativa sequentis. Declarativa superioris fit subjec-
tiva sequentis, ut Omnis voluptas bonum est ; omne bonum utile
est; omnis igitur voluptas utilis est. Subjectiva superioris fit de-
clarativa sequentis, si hoc modo velis convertere : Omne bonum
utile est ; omnis voluptas bonum est; omnis igitur voluptas utilis
est."
In First Form or Figure, notices the four direct and five indirect
moods, — reflexion : and in the second and third, the usual number
of moods.^
In Second Figure — " Hie reflexione si utaris, alius modus non
efficitur, quoniam de utrisque subjectivis fit illatio." He seems
to hold that two direct conclusions are competent in Second and
Third Figures.
In Second Figure, he enounces generally (four times) as thus : —
a Flourished A.c. 457, Passow ; 474, See Dialect., Opera, TpTp.BZS, 556, Genev.
Tennemann. 1650, and above, p. 404. (fl. 520). Cf.
/3 Cassiodorus, in First Figure, gives Apuleius, Be Syllogismo Categorko, Op.,
both forms, "velsic;" in Second and p. 35. Elmen. (a.c. 160.) Isidorus, of
Third, though he gives also an " vel sic," Seville, {Gothofr. A uct., p. 878) (a.c. 600 ;
they ai-e examples, both in converse, of died 636.)
Capella's general mode of enunciation.
APPENDIX. 425
" Omne justum honestum; nullum turpe honestunn; nullum igitur
justiiTYi turpe ; but sometimes (once) thus, — "Nullum igitur turpe
justum."
In Third Form or Figure generally (six times) thus as — " Omne
justum honestum ; omne justum bonum ; quoddam igitur hon-
estum bonum ;" but sometimes (once) as, — ^'Quoddam igitur
bonum JionestuTn."
VI. — ISIDOEUS.
Isidorus, Originum, L. i. c. 28. Be Syllogismis Dialecticis.
Opera, p. 20 (1617) ; in Gothofred. Auctores, p. 878.
"Formulae Categoricorum, id est, Praedicativorum SyUogis-
morum sunt tres. Primae formulse modi sunt novem.
" Primus modus est qui conducit, id est, qui coUigit ex uni-
versalibus dedicativis dedicativum universale directim : ut,
Omne justum honestum ; omne honestum bonum ; ergo omne
justum bonum." All in first figure, with minor first ; in second
and third figures, varies ; uses per reflexionem et reflexim in-
difierently ; and through all moods of all figures follows Apuleius.
" Has formulas Categoricorum Syllogismorum qui plene nosse
desiderat, librum legat qui inscribitur Perihermenias Apideii, et
quse subtilius sunt tractata cognosced "
VII. — AVEEEOES.
Averroes, In Anal. Prior., L. i., c. v., on First Figure : "If,
therefore, the middle term be so ordered between the two ex-
tremes, that it be predicated of the minor and subjected to the
major, (as, if we say all C is B and all B is A) ; it is plain that
this order of syllogism is natural to us ; and it is called by Aris-
totle the first figure." And thus are stated all the examples in detail.
C vi. Figure Second. — " And the proposition whose subject is
the subject of the qusesitum is the minor proposition, but that
whose subject is the predicate of the qusesitum is the major. Let
us then place first in order of enunciation the minor extreme ; let
the middle term then follow, and the major come last, to the end
that thus the major may be distinguished from the minor ; for in
this figure the terms are not distinguished, unless by relation to
the qupesitum." So all the examples.
C. vii. Third Figure. — " That proposition in which lies the sub-
426 APPENDIX.
ject of the qusesitura is called the minor proposition, since the
subject itself is called the minor term ; that proposition which
contains the predicate of the quassitum is named the major. In
the example, let the minor term be C, the middle B, and the major
A, and their order be that we first enounce the middle, then the
minor, and last of all the major." And so the examples.
VIII. — Melanchthon.
Melanchthon, Erotemata Dialecticce, L. iii., p. 175.
" Demonstration why there are necessarily three [and only three]
Figures.
" Every argumentation which admits the syllogistic form, (for of
such form Induction and Example are not recipient, [?]) proceeds
either [1°], Erom genus to species universally with an universal
conclusion, or [2°], From species to genus with a particular conclu-
sion, or [3°], A distraction of two species takes place, or [4°], There
is a concatenation of a plurality of causes and effects. Nor are
there more modes of argumentation, if we judge with skill.
" The process from genus to species engenders the First Figure.
And the consequence is valid from the genus with a universal sign
both affirmatively and negatively to the species,— this is naturally
manifest. The process from species to genus with a particular
conclusion engenders the Third Figure. And it is evident that,
the species posited, the genus is posited.
" The distraction of species engenders the Second Figure. And
the reason of the consequence is clear, because disparate species are
necessarily sundered. These may be judged of by common sense,
without any lengthened teaching. Both are manifest, — that the
figures are rightly distributed, and that the consequences are in-
dubitably valid."
IX. — Aenauld.
Arnauld, L'ArtdePenser, {Port Royal Logic), P. iii., ch. 11, p.
235. — General principle of syllogisms : — " That one of the pre-
mises should contaifi the conclusion, and the other shoiu that it
does so contain it." — [So Purchot, Instit.Fhil., Vol. I. P. iii., ch. 1,]
Ch. v., p. 215. — "Foundation of First Figure.
" Principle of affirmative moods -.—That what agrees with a
notion taken universally, agrees also with all of which this notion
is affirmed ; in other words, with all that is the subject of this
APPENDIX. 427
notion, or is comprised within its sphere." [Or, more shortly,
(says Purchot, c. vi.). Whatever is predicated of the superior, is
predicated of the inferior.']
" Principle of the negative moods : — What is denied of a notion
taken universally, is denied of all whereof this notion is affirmed!'
[Purchot — What is repugnant to the superior, is repugnant also
to the inferior, eh. vL, p. 217.]
" Foundation of the Second Figure.^' Principle of the syllogisms
in Cesare and Festino : — That what is denied of a universal
notion, is denied also of whatever this notion is affirmed, that is
to say, of all its subjects.
" Principle of the syllogisms of Camestres, Baroco : — All that is
contained under the extension of a universal notion, agrees luith
none of the subjects luhereof that notion has been denied, seeing
that the attribute of a negative proposition is taken in its whole
extension."
Ch. vii. p. 220. " Foundation of the Third Figure.
" Principle of the affirmative moods : — When two terms may he
affirmed of the same thing, they may also be affirmed of each
other, taken particidarly. [So Purchot nearly.]
"Principle of the negative moods: — When of two terms^ the
one may be denied, and the other affirmed, oftliesame thing, they
may be particidarly denied of each other. ^' [So Purchot nearly.]
No foundation or principle given for the Fourth Figure.
X. — Grosser.
Samuelis Grosseri, Pharus Intcllectus, 1697, P. iii., S. i., Mem.
3, c. 2 (probably from Weiss, see Pref ) " The foundation of the
first figure is the Dictum De Omni et Nullo ; for whatever is uni-
versally affirmed or denied of a universal subject, that is also
affirmed or denied of all and each contained under that subject.
"The foundation of the second figure is Contrariety; for the
predicates of contrary things are contrary.
" The foundation of the third figure is the agreement of the ex-
tremes in any third ; for what agrees with any third agrees with
each other, and may be joined or separated in the same proposition,
inasmuch as they are in agreement or confliction in relation to any
third thing."
« Purchot says this Figure rests upon same, hut something agrees tvith the one,
single principle — 2\vo things are nut the which is repugnant to the other.
428 APPENDIX.
Illustrates the three figures by three triangles, p. 132. In
the first we ascend to the apex on one side, and descend on the
other ; in the second we ascend at both sides ; in the third we
descend on both sides.
XI. — Lambert.
Lambert, Neues Organon, Vol. I., § 225. — See Melanchthon,
(above p. 426).
Relation of Figures. " We further remark that the first dis-
coverer of Syllogisms and their Figures was, in his arrangement of
their propositions, determined by some arbitrary circumstance ; his
views and selections at least were not founded on aught natural and
necessary (§ 196). He places, to wit, that premise after the other,
which contains among its terms the subject of the conclusion, pro-
bably in order to introduce into all the figures a common law. To
that law, however, we do not restrict ourselves either in speech or in
writing. The mathematician, who perhaps draws the greatest num-
ber of formal syllogisms with the fewest paralogisms, commences
to take the first figure, for example, not with the major but with
the minor proposition, because not only in this figure is such pre-
mise always the more obtrusive, but also because its subject is the
proper matter of discourse. Frequently the premise is only quoted,
or it is absolutely omitted whensoever it is of itself obvious to the
reader, or is easily discoverable from the minor and conclusion.
The conclusion inferred is then, in like manner, constituted into the
minor proposition of a new syllogism, wherewith a new major is
connected. This natural arrangement of the syllogisms of the first
figure, rests, consequently, altogether on the principle, — That tve can
assert of the subject of an affirmative proposition, whatever we
may know of its predicate ; or tvhat may he said of the attribute
of a thing is valid of the thing itself And this is what the syl-
logisms of the first Figure have peculiar to themselves. It is also
so expressed ; — What is true of the genus is true also of each of
its species.
§ 226. " On the other hand, in the second and third Figures there
is no talk of species and genera. The second Figure denies the
subjects of each other, because they are diverse in their attributes;
and every difierence of attribute is here effectual. We, conse-
quently, use this figure principally in the case where two things
APPENDIX. 429
ought not to be intercommuted or confounded. This becomes
necessarily impossible, so soon as we discover in the thing A some-
thing which does not exist in the thing B. We may, consequently,
say that syllogisms of the second figure lead us to distinguish
things, and prevent us from confounding notions. And it will be
also found, that, in these cases, we always use them.
§ 227. " The third Figure affords Examples and Exceptions; and,
in this Figure, we adduce all exempla in contrarium. The two
formula are as follows : —
"1. There are B %vhich are C; for M is B and C.
" 2. There are B tuhich are not C / for M is B and not C.
" In this manner we draw syllogisms of the Third Figure, for the
most part, in the form of copulative propositions (§ 135) ; because
we are not wont twice to repeat the subject, or to make thereof
two propositions. Sometimes one proposition is wholly omitted,
when, to mt, it is self-manifest.
"In the Fourth Figure, as in the First, species and genera ap^Dear
only with this difference, that in the moods, Bai^alvp, Dibatis,
Fesapo, Fresison, the inference is from the species to the genus ;
whereas in Calentes there is denied of the species what was denied
of the genus. For where the genus is not, neither are there any
of its species. This last mood we, therefore, use when we conclude
negatively a minori ad majiis, seeing that the genus precedes, and
is more frequently presented than, any of its species.
§ 229. " The syllogisms of the four Figures are thus distinguished
in relation to their employment, in the following respects : —
" 1. The First Figure ascribes to the thing what we know of its
attribute. It concludes from the genus to the species.
" 2. The Second Figure leads to the discrimination of things, and
relieves perplexity in our notions.
" 3. The Third Figure affords examples and exceptions in pro-
positions which appear general.
" 4. The Fourth Figure finds species in a genus in Baralip and
Dibatis ; it shows that the sj)ecies does not exhaust the genus in
Fesapo, Fresison ; and it denies the species of what was denied
of the genus in Calentes.
§ 230. " This determination of the difference of the Four Figures
is, absolutely speaking, only manifested when we employ them
after natural fashion, and without any thought of a selection. For,
430 APPENDIX.
as the syllogisms of every figure admit of being transmuted into
those of the first, and partly also into those of any other, if we rightly
convert, or interchange, or turn into propositions of equal value,
their premises ; consequently, in this point of view, no difference
subsists between them ; but whether we in every case should perform
such commutations, in order to bring a syllogism under a favourite
figure, or to assure ourselves of its correctness, — this is a wholly
different question. The latter is manifestly futile. For, in the
commutation, we must always undertake a conversion of the pre-
mises, and a converted proposition is assuredly not always of
equal evidence with that which we had to convert, while, at the
same time, we are not so well accustomed to it ; for example, the
proposition. Some stones attract iron, every one will admit, be-
cause The magnet is a stone, and attracts iron. This syllogism is
in the Third Figure. In the first, by conversion of one of its pre-
mises, it would run thus : —
Major, — All magnets attract iron ;
Minor, — Some stones are magnets ;
Conclusioa, — Some stones attract iron.
Here we are unaccustomed to the minor proposition, while it ap-
pears as if we must pass all stones under review, in order to pick
out magnets from among them. On the other hand, that the
magnet is a stone, is a proposition which far more naturally sug-
gests itself, and demands no consideration. In like manner, A
circle is not square; for the circle is round, — the square not. This
proof [in the third figure] is as follows, when cast in the first : —
What is not round is no circle ;
A square is not roimcl ;
Consequently, &c.
Here the major proposition is converted by means of terminus infi-
nitiis, and its truth is manifested to us only through the conscious-
ness that all circles are rcmnd. For, independently of this pro-
position, should we not hesitate, — there being innumerable things
which are not round, — whether the circle were one of those which
belonged to this category ? We think not ; because we are aware.
§ 231. " It is thus apparent that we use every syllogistic figure
there, where the propositions, as each figure requires them, are
more familiar and more current. The difference of figures rests.
APPENDIX. 431
therefore, not only on their form, bnt extends itself, Ly relation to
their employment, also to things themselves, so that we use each
figure where its use is more natural : The first for finding out or
'proving the Attributes of a thing ; the second for finding out or
proving the Difference of things ; the third for finding out and
proving Examples and Exceptions ; the fourth for finding out
and excluding the Species of a Genus.
§ 232. " Further, whether the three last figures are less evident
than the first, is a question which has been denied [affirmed (?)] on
this account, that the first figure only rests immediately on the
Dictum de Omni et Nulla [§ 220], whilst the others have hitherto,
by a circuit, been educed therefrom. We have already remarked
[§ 211], that this circuit, through our mode of notation, is wholly
superseded. We need, therefore, only translate its principle into
the vernacular, and we shall find that the Dictum, de Omni et Nulla
is on that account applicable to the first figure, because its truth
is based on the nature of the proposition. From this principle,
therefore, the first figure and its moods admit of an immediate de-
duction ; it is thus only a question whether the other figures are
incapable [capable (?)] of such immediate deduction, or whether it
is necessary previously to derive them through the first figure ?
Our mode of notation shows that the latter is an [unnecessary] cir-
cuit, because every variety of syllogism admits for itself a various
notation, and because, in that case, the j^remises are taken for what
they actually are. Consequently, every figure, like the first, has its
own probation, — a probation drawn exclusively from the natures of
the propositions. The whole matter is reduced to this, — Whether
a notion, wholly or in part, is, or, wholly or in part, is not, under
a second ; and whether, again, this second, ivh oily or in part, is,
or, wholly or in part, is not, under a third. All else proceeds only
on the interchange of equivalent modes of expression, — the figured,
namely, and those which are not figured. And this interchange
we may style translating, since the figured modes of expression may
be regarded as a special language, serving the purpose of a nota-
tion. We have above (§ 220), after all the syllogistic modes were
discovered and denoted, adduced the Dictum de Omni et Ntdlo,
but only historically, since our manner of determining the syllogis-
tic moods is immediately founded on the nature of the propositions,
from which this Dictum is only a consequence. Moreover, this
432 APPENDIX.
consequence is special, resting, as it does, on the notions of Species
and Genera. Wherefore, its validity only extends so far as pro-
positions can be recalled to these notions ; as, for example, in
the First Figure. In the Second, the notion of Difference emerges ;
and in the Third, the notion of Example. If we, therefore, would
have special dicta for the several Figures, in that case it would
follow, and, at the same time, become manifest that the middle
term of a syllogism, considered for itself, expresses, in the First
Figure, a principle [of Ascription or Procreation^ ; in the Second,
Difference ; in the Third, an Example; and in the Fourth, the
principle of Reciprocity.
1. For the First Figure. Dictum de Omni et Nullo. What is
true of all A, is true of every A.
2. For the Second Figure. Dictum de Diverso. Things which
are different, are not attributes of each other.
3. For the Third Figure. Dictum de Exemplo. When we find
things A which are B, in that case some A are B.
4. For the Fourth Figure. Dictum de Reciproco. I. If no M
is B ; then no B is this or that M. II. If C is [or is not] this or
that B ; in that case some B are [or are not] C."
XII. — Platner.
Platner, Philosophische Aphorismcn, 3d ed., 1793. — Part I., §
544, conformed to his Lehrhuch der Logik und Metaphysik, 1795,
§ 227. " The reason why the predicate belongs to the subject is in
all possible syllogisms this, — because the subject stands in a relation
of subordination with, [is either higher or lower than], a third
notion to which the predicate belongs. Consequently, all inference
proceeds on the following rule : — If the subject of the [concluding]
judgment stand in a relation of subordination with a third notion,
to which a certain predicate pertains ; in that case, this predicate
also pertains to the same judgment, affirmatively or negatively."
In his note on this Aphorism, Platner {Lehrhuch) admits — "My
fundamental rule is only at fault in the second Aristotelic figure,
which, however, is no genuine figure ; because here, in the pre-
mises, the subject and predicate have changed places," &c. In the
2d edition of his Aphorisms (1784) he had adopted the principle of
Identity with the same third, as he has it : " In what extension
or proportion (Maasse) two notions are like or unlike to a third,
APPENDIX, 433
in the same extension or iwopoi'tion are they like or unlike each
other." (§ 628.)
Philosophische Aphorismen, Part I., third edition, 1793,
§ 568, compared with second, 1784, § 672-676. — " Nevertheless,
each of these grammatical figures of syllogism has its peculiar
adai^tation in language for the dialectical aj^plication of proofs ;
and the assertion is without foundation, that the first is the most
natural. Its use is only more appropriate, when we intend to show,
— that a p)redicate pertains \or does not jiertain'] to a subject in
virtue of its class. More naturally than in the first, do we show,
in the second, the difference of things apparently similar ; and in
the third, the similarity of apparently different things. The
fourth figure, [it is said in the second edition], on account of the
position of its terms, is always unnatural in language."
Philosophische Aphorismen, Parti., last edition, 1793, § 561. —
" The principle of the first figure is the Dictum de Omni et Nullo.'"
§ 564. — " Touching the other figure, [the third, for in this edi-
tion Platner abolishes, in a logical relation, the second], its special
principle is the following rule : — What belongs to the subordinate,
that, since the subordinate is a part of the universal, belongs also
in jKirt {particularly) to the universal."
In the second edition, 1784, the second figure is recognised,
and, with the third, obtains its special law.
§ 659. — " The principle of the second figure is : — // tiuo notions,
wholly or in part, are opposite to a third, so are they also, wholly
or in part, op)posite to each other."
§ 664. — "The principle of the third figiu'e is : — What can he
jxirticulaidy affi^rmed or denied of a subaltern species.^ that also,
in so far as such subaltern species is part of a genus, may be
p)articidarly affirmed or denied of the genus."
Philosophische Aphoi^ismen. Part I., § 546. Note. — " In
general, logicians treat the subject as if it were necessarily subordi-
nated to the predicate. It may, however, on the contrary, be the
higher notion, and the predicate thus be subordinated to it. This
is the case in all particular propositions where the predicate is not
an attribute of the genus, but an accident of the subject. For
instance, — Some creatures are animals; here the subject is the
higher : Somie men are imperfect ; here the higher is the predi-
cate. We must not, therefore, in our syllogistic, thus enounce the
VOL. II. 2 E
434 APPENDIX.
fundamental rule of reasonings, — If the subject he subordinated to
a third notion, but with or in the relation of subordination with
a third notion^
XIII— Fries.
Fries, System der Logik, § 56. — " The species of categorical syl-
logisms are determined by tlie variety of relations in which three
notions may stand to each other, so that a syllogism may be the
result.
" These relations may be thought as three.
" Case I. — Three notations are reciprocally subordinated in gra-
dation, so that the second is subordinated to the first, but super-
ordinated to the third.
" Case II. — Two notions are subordinated to a third.
" Case III. — Two notions are superordinated to a third.''
" When, in these cases, is a syllogism possible ?
§ 57. — " In all the three cases, the syllogisms are equally valid,
for they are fomided on the general laws of the comiection of
notions.
" They all follow, to wit, from the relation of a whole sphere to
its parts, which lies in the Dictum de Omni et Nullo. The prin-
ciples for the three mentioned cases are thus : — ■
" For the first, — The part (C) of the part (B) lies in the whole
(A), and what (A) lies out of the whole (B), lies also out of the
part (C).
" For the second, — What (A or some A) lies out of the whole (B),
lies also out of its parts (C).
" For the third, — If a part (B) lie in two wholes (A and C), in
that case these have a part in common; and if a part (B) lie in a
whole (C), but out of another whole (A), in that case the first (C)
has apart out of the other (A).
" The first case alone coincides immediately with the perfect de-
claration of a syllogism, — that a case is therein determined by a
rule. For the third case, therefore, our two declarations of a
major premise, — that it is the rule, and that it contains the major
term, — do not coincide, seeing that here the minor term may be
forthcoming in the rule. On this account, the arrangement of the
« [See Jordano Bruno (in Denzinger, § 237, p. 163].
Logik, t. ii., p. 259). Stattler, Logica,
APPENDIX. 435
first case is said to be the only regular, and the others are reduced
to it. That this reduction is easily possible, we may in general
convince ourselves, by reflecting that every syllogism requires a
general rule as premise, and that the other cases are only distin-
guished from the first by the converted arrangement of the propo-
sitions. But as all propositions may be either purely converted or
purely counterjiosed, consequently the two last cases can at most
so far deviate from the first, that they are connected with the first
case only through reversed {gegentheilige) notions.
§ 57 b. " The doctrine of the several species of categorical syllo-
gisms, as regulated by the forms of their judgmeuts, is at bottom
an empty subtlety ; for the result of all this circuity is only, that, in
every categorical syllogism, a case is determined by a rule, and this
is already given in the law, that in every reasoning one premise
must be universal. The scholastic logic treats of this doctrine
only in so far as the species of syllogism are determined by the
forms of judgment, and thereby only involves itself in long gram-
matical discussions. Aristotle has been falsely reproached for
overlooking the fourth figure, he only having admitted three. For
Aristotle proceeds, precisely as I have here done ; only on the rela-
tion of notions in a syllogism, of which there are possible only our
three cases. His error lies in this, — that he did not lay a general
rule at the root of every figure, but, with a prolixity wholly useless,
in determining the moods of the several figures, details each,
even of the illegitimate, and demonstrates its illegitimacy. This
prolixity has been too often imitated by other logicians, in the
attempts at an evolution of the moods. Kant, goes too far, in de-
nouncing this whole doctrine as a mere grammatical subtlety. The
distinction of the three cases is, however, a logical distinction ; and
his assertion, that the force of inference in the other two is wholly
derived from that of the first case, is likewise not correct. I mani-
festly, however, conclude as easily in the third case, — 'A part
which lies in two wholes, is a part common to both,' — as in the
first, — 'The part of the part lies in the whole.' The third case
presents, indeed, the readiest arrangement for reasonings from the
particular to the general, i. e., for syllogisms in the second figure
according to our terminology.
" The scholastic doctrine of the four syllogistic figures and nine-
teen moods of categorical syllogisms requires no lengthened illus-
436 APPENDIX.
tration. If the figures are determined by the arrangement of
notions in the premises, then the following combination is exhaus-
tive. For the conclusion in all cases S P [being supposed the
same], the [terms or] notions stand :
1) According to our first case, M P
S M
2) With converted major premise, P M
S M
3) With converted minor premise, M P
M S
4) Both premises converted, P M
M S
" Should we therefore simply convert both jjremises in a syllo-
gism of the first figure, we are able to express it in all the figures.
Let the notions given be fireproof] lead, metal, there then follows
the conclusion — Some metal is not fireproof— from, the premises : —
In the First Figure — iVo lead is fireproof ;
tSome 7netal is lead ;
In the ^QQOixOLY\gwxQ^Not]img fireproof is lead ;
Some metal is lead ;
In the Third Figure — No lead is fitrj^roof;
A II lead is metal ;
In the Fourth YigViVQ— Nothing fireproof is lead,
All lead is metal.
" It is here apparent that the three first figures are oui' three
cases ; but the fourth we did not employ, as it contains no peculiar
relations or notions, but only under our first case superordinates,
and then subordinates a middle term. This manner of enunciating
a syllogism is thus only possible, where we are competent, through
conversions, to transmute the arrangement of the first figure into
that of the fourth. Now this happens : 1] If we convert the con-
clusion S P into P S, since then the major and the minor
terms, as also the major and minor premises, change names; or, 2]
If both premises allow of an immediate conversion, so that the one
remains universal ; for then the converted propositions contain the
same thoughts as those given, and, consequently, establish the same
conclusion."
[Objections to Fries' doctrine of figure — 1°, Only applies to affir-
matives ; 2°, Only the arrangement of the results of a successful
comparison, and takes no heed of the comparisons that may have
APPENDIX. 437
been fruitless, (the illegitimate moods) ; 3°, Takes accomit of only
one subordination, for, in second and third cases, in each there is
a reciprocal subordination in Extension and Comprehension.]
XIV and XV. — Keug and Beneke — theie Docteines of
Syllogism ceitigised.
The authority" of the two following philosophers, who conclude
this series, is rather negative than j)Ositive ; inasmuch as they
both concur in proving, that the last attempts at a reformation of
the Syllogistic Theory proceed on a wholly different ground from
that on which, I think, this alone can be accomplished. These two
philosophers are Krug and Beneke ; for, beside them, I am aware
of no others by whom this has been attempted.
Krug was a disciple of the Kantian school, Kant's immediate
successor in his Chair of Logic and Metaphysics at Koenigsberg,
and, subsequently, Professor of Philosophy in the University of
Leipsic. He is distinguished, not only as a volmninous writer, but
as a perspicuous and acute thinker ; and his peculiar modification
of the Kantian system, through a virtual return to the principle of
Common Sense, is known, among the German theories, by the
name of Synthetism. His Logic, (the first part of his System of
Theoretical Fhilosoj^hy), was published in 1806, and is one of the
best, among the many excellent, treatises on that science, which we
owe to the learning and ability of the Germans. (I have before me
the fourth edition, that of 1833.) Krug propounded a new theory
of syllogistic ; but the novelty of his scheme is wholly external,
and adds only fresh complication to the old confusion. It has,
accordingly, found no fiivour among subsequent logicians.
Passing over the perverse ingenuity of the principles on which
the whole doctrine is founded, it is enough to state, that Krug dis-
tributes the syllogistic moods into eight classes. Of these the first,
(which, with some other logicians, he considers not as a figure at all,
but as the pure, regular, and ordinary form of reasoning), corre-
sponds to the First Figure of the Aristotelico-Scholastic distribu-
tion. The other seven classes, as so many impure, irregular, and
extraordinary forms, constitute, (on the analogy of Rhetoric and
Grammar), so many figures. Of these, the new is only the old
First Figure, the minor premise, in extension, being stated before
the major. Krug, like our other modern logicians, is not aware
438 APPENDIX.
that this was the order in which the syllogism was regularly cast,
in common language, by the Greeks, by the Arabians, by the Jews,
and by the Latins prior to Boethius." The old and new first figures
are only a single figure, the syllogism being drawn in the counter
orders of breadth and of depth. A mood in these orders, though
externally varying, is intrinsically, — is schematically, — the same.
Krug's distinction of his new first figure is, therefore, null. Thus,
Barama is Barbara; Caleme isCelarent; Dirami is Darii; Firemo
is Ferio. Nor is his discrimination of the other six better founded.
His new (the old) Second, and his FiftJt Figures, are also one.
The latter is precisely the same with the former ; Fimeso is
Festino, and Fomaco is Baroco. In one case, (under Camestres),
Krug adopts, as alone right, the conclusion rejected by the logi-
cians. In this, he and they are, in fact, both wrong ; though in
opposite ways. Each mood, in the second, (as in the third), figure,
has two indifferent conclusions ; and the special one-sided practice
of the former is only useful, as gainsaying the general one-sided
precept of the latter. The same objection applies to Krug's new
(the old) Third, in connection with his Sixth Figure. They are
one ; Daroco is Bocardo, Fapimo is Felapton, and Fisemo is
Ferison. In two cases, (under Disamis and Bocardo), Krug has
recognised the repudiated conclusion. Krug (§ 109) has, how-
ever, committed an error in regard to Bocardo. He gives, as its
example, the following syllogism, in which, for brevity, I have
filled ujj the quantifications :
" Some animals are not [an//] viviparous ;
All animals are [some] orcjanised things ;
Therefore, some organised things are not [ani/] viinparous."
In a note, he adds : " The conclusion should here be : — ' There-
fore, some things which are not viviparous are [some] organised.'
And this is seen also by reduction. We have, however, followed
the arbitrary precept of the logicians, that the extreme in the
second proposition should stand subject in the conclusion ; although
it be here indifferent, which extreme becomes the subject. The
conclusion is only changed into another quality." Only changed
into another quality ! Only an affirmative conclusion from a
negative premise ! The legitimate inference is : —
a See above, p. 403. — Ed.
APPENDIX. 439
" Therefore, no vivijmrous is some organic ; " or,
" Therefore, any viviparous is not some organic.^'
Bachmann, [Logik, § ] 35), anotlier eminent logician, has erred
with Krug. A particular predicate in a negative proposition, seems
indeed one of the last difficulties for reformed logic. Krug's new
(the old) Fourth Figure bears a corresponding relation to his
Seventh. He is right, certainly, in abolishing all the moods of the
fourth figure, except Fesapo and Fresiso ; and, from his point of
view, he is hardly to be blamed for not abolishing these likewise,
along with the correlative moods, Fapesmo and Fi^isesmo, and,
with them, his seventh figure. Finally, rejecting the scholastic
doctrine of Reduction, he adopts, not without sundry perverse
additions, Kant's jjlan of accomplishing the same end ; so that
Krug's conversive and contrapositive and transpositive interpola-
tions, by which he brings back to propriety his sevenfold figured
aberrations, are merely the substitution of one " false subtlety " for
another. He, and Bachmann after him, renounce, however, " the
crotchet of the Aristotelians," in making the extreme of the prior
premise the predicate, always, of the conclusion, in the first and
second figures ; and, though both do this partially and from an
erroneous point of view, their enunciation, such as it is, is still
something.
Professor Beneke, of Berlin, is the last to whom I can refer,
and in him we have, on the point in question, the final result of
modern speculation. This acute and very original metaphysician
stands the uncompromising champion of the philosophy of experi-
ence, against the counter doctrine of transcendentalism, in all its
forms, now prevalent in Germany ; and, among the other depart-
ments of mental science, he has cultivated the theory of reasoning,
with great ability and success. In 1832 appeared his Lehrhuch
der Logik, &c.; in 1839, his Syllogismorum Analyticorum Ori~
gines et Or do Naturalis, &c. ; and in 1842, his System der Logik,
&c., in two volumes. In Logic, Beneke has devoted an especial
share of attention to the theory and distribution of Syllogism ; but
it is precisely on this point, though always admiring the ingenuity
of his reasonings, that I am compelled overtly to dissent from his
conclusions.
440 APPENDIX.
The Syllogistic of Beneke is at once opposed, and correspondent,
to that of Krug ; there is an external difference, but, without imi-
tation, an internal similarity. Instead of erroneously multiplying
the syllogistic figures, like the Leipsic philosopher, the philosopher
of Berlin ostensibly supersedes them altogether. Yet, when con-
sidered in essence and result, both theories agree, in being, and
from the same side, severally, the one an amplification, the other
an express doubling, of the nineteen scholastic moods. In this,
both logicians were unaware, that the same had been, long ago,
virtually accomplished in the progress of the science ; neither con-
sidered, that the amplification he proposed was superficial, not to
say mistaken ; and that, instead of simplicity, it only tended to
introduce an additional perplexity into the study. Beneke has the
merit of more openly relieving the opposition of Breadth and
Depth, in the construction of the syllogism ; and Krug, though on
erroneous grounds, that of partially renouncing the old error of
the logicians in regard to the one syllogistic conclusion, in the
second and third figures. But, in his doctrine of moods, Beneke
has, I think, gone wrong in two opposite ways : like Krug, in his
arbitrary multiplication of these forms ; like logicians in general,
in their arbitrary limitation.
In regard to the former, — the counter quantities of Breadth and
dej)th do not discriminate two moods, but merely two ways of
stating the same mood. Accordingly, we do not multiply^ the
moods of the first figure, to which alone the principle applies, by
casting them in the one dependency and in the other; we only
show, that, in that figure, every single mood may be enounced in a
twofold order, more german, the one to the quantity of extension, the
other to the quantity of intension. An adequate notation ought,
equally and at once, to indicate both. But in reference to the
second and third figures, the case is worse. For in them we have
no such dependency at all between the extremes ; and to double
their moods, on this principle, we must take, divide, and arbitrarily
appropriate, one of the two indifferent conclusions. But, as every
single mood of these figures has a double conclusion, this division
cannot be made to difference their plurality. If Professor Beneke
would look (instar omnium) into Apuleius or Isidorus, or, better
than either, into Blemmidas, he will find all his new moods, (not,
APPENDIX. 441
of course, those in tlie fourth figure) stated by these, as by other
ancient logicians ; wlio, however, dreamed not that the mere acci-
dental difference of, what they called, an analytic and synthetic
enounceraent, determined any multiplication of the moods them-
selves.
In the latter respect, Dr Beneke has only followed his predeces-
sors ; I, therefore, make no comment on the imperfection. But, in
accomplishing what he specially proposes, whilst we do not find
any advancement of the science, we find the old confusion and
intricacy rej^laced by another, perhaps worse. To say nothing of
his non-abolition of the fourth figure, and of his positive failures
in doubling its moods ; the whole process is carried on by a series
of arbitrary technical operations, to supersede which must be the
aim of any one who would reconcile Logic with nature. His new
(but which in reality are old) amplifications are brought to bear
(I translate his titles) through " Commutations of the Premises, —
by Subalternation, — by Conversion, — by Contraposition ; " and "of
the Major, — of the Minor," — in fact of both premises, {e.g. Fesajw,
&c.). And so difficult are these j^rocesses, if not so uncertain the
author's language, that, after considerable study, I am still in doubt
of his meaning on more points than one. I am unable, for ex-
ample, to reconcile the following statements : — Dr Beneke repeatedly
denies, in conformity with the common doctrine, the universal
quantification of the predicate in affirmative propositions ; and yet
founds four moods upon this very quantification, in the conver-
sion of a universal affirmative. This is one insolubility. But there
arises another from these moods themselves (§ 28-81). For, if we
employ this quantification, we have moods certainly, but not of the
same figure with their nominal correlatives ; whereas, if we do not,
simply rejecting the permission, all slides smoothly, — we have the
right moods in the right figure. This, again, I am unable to solve.
Dr Beneke's duplication of the moods is also in sundry cases only
nominal ; as is seen, for example, in Ferio 2, Fesapo 2, and Fre-
siso 2, which are forms, all, and in all respects, identical. I must
protest also against his violence to logical language. Thus, he
employs everywhere "non omne," "non omnia," "alle sind nicht,"
&c., which is only a particular, (being a mere denial of omnitude),
for the absolute or universal negative, " nullum," " nulla," " kein
442 APPENDIX.
ist," no, none, not any, &c., in opposition both to principle, and to
the practice of Aristotle and succeeding logicians.
[XVI.— TiTius.
Gottlieb Gerhard Titius, Ars Gogitandi, sive Scientia Cogita-
tionum Gogitantium, Gogitationibus Necessai^is Instructa et a
Peregrinis Liherata. Leipsise, 1723, (first edition, 1701).
Titius has been partially referred to by Sir W. Hamilton, as
having maintained the doctrine of a Quantified Predicate. See
above, p. 312. His theory of the Figure and Mood of Syllogism
is well deserving of notice, — proceeding, as it does, on the applica-
tion of that doctrine. This theory is principally contained in the
following extracts from his Ars Gogitandi, which show how closely
he has approximated, on several fundamental points, to the doc-
trines of the New Analytic.'^
Titius gives two canons of syllogism : —
I. Affirmative. " Qusecunque conveniunt in uno tertio, ilia
etiam, juxta mensuram illius convenientise, inter se conveniunt."
II, Negative. " Qusecunque pugnant in certo aliquo tertio, ilia,
juxta mensuram illius disconvenientise, etiam inter se pugnant."
C. ix. §§ 30, 27.
The following relates to his doctrine of Figure and Mood, and
to the special rules of Syllogism, as commonly accepted : —
C. X. § i. " Sic igitur omnium Syllogismorum formalis ratio in
genuina medii termini et prpedicati ac subject! Conclusionis colla-
tione consistit ; eam si dicere Ye\\ii forniam essentialem, aut figu-
ram generalem vel communem, non valde reluctabor.
§ ii. " Prseter eam vero Peripatetici Figurxis ex peculiari medii
termini situ adstruunt, ea ratione ut Primani figuram dicant, in
qua medius terminus in Majore est subjectum, in Minore Prredica-
tum, Secundam, ubi idem bis prsedicati, et Tertiam, ubi subjecti
locum bis subit. Galenus adjecit Quartam primes contrariam, in
qua medius terminus in majore est prredicatura, in minore subjec-
tum, quam pluribus etiam exposuit Autor. Art. Gog. p. 3, c. 8.
a. For Titius' doctrine of a Quantified thetical Syllogism, see .above, pp. 312,
Predicate, its application to the Conver- 274, 375.- Ed.
sion of Propositions and to the Hypo-
APPENDIX. 443
§ iii. " Cseterum illae figurse tantura sunt accidentales, ab iisque
vis conchidendi iion dependet. Quodsi tamen quis diversum medii
termini situm attendendum esse putet, turn nee Quarta figura negii-
genda esse videtur, licet earn Peripatetici nonnulli haut curandam
existiment, vide Ulman. Synops. Log. 1. 3, c. 2, p. J 64.
§ iv. " Interim Pi^ima Cfeteris magis naturalis ex eo videri
potest, quod Subjectum et Prsedicatum Conclusionis in Prsemissis
suam retineat qualitatem, cum in secunda et tertia alterum quali-
tatem suam exuere, in quarta vero utrumque earn deponere debeat.
§ V. " Postea in unaquaque figura, pro ratione quantitatis et quaii-
tatis propositionum, peculiares Modi adstruuntur, ita quidem ut
Primje figuree Qiiatuor, totidem Secundse, Terti?e sex attribuantm-,
ex quibus etiam debite variatis Quarta quinque accipiat, prout ilia
passim cum vocabulis memorialibus recenseri solent, ut ilia quidem
hue transcribere opus non sit, vide Autor, Art. Cogit., p. 3, c. 5,
6, 7, 8.
§ vi. "Non opus esse istis figuris et modis ad dijudicandam
Syllogismorum bonitatem, ex monito § 3, jam intelligi potest.
Quomodo tamen sine iis bonitas laudata intelligi queat, id forte
non adeo liquidum est
§ vii. " Non diu hie quserenda sunt remedia : Observetur forma
essentialis seu figura communis, ac de veritate Syllogismi recte
judicabitur. Applicatio autem hujus moniti non est diflicilis, nam
primo rcspiciendum ad conclusionem, deinde ad medium terminum,
quo facto etiam j udicari potest, an ejus et terminorum conclusionis
collatio in prsemissis recte sit instituta nee ne
§ ix. " De c?etero uti anxie jam non inquiram, an omnis bene
concludendi ratio numero modorum denario circumscribatur,
quod quidem juxta aKpi^eiav mathematicam demonstrasse videri
vult Autor. Art. Cog. p. 3, c. 4, ita id haut admiserim, quod illi
modi, quos vulgo laudant. Primes, Secundse aut Tertiag figurse prae-
cise sint assignandi, licet hoc itidem acumine matheraatico se de-
monstrasse putet dictus Autor. d. I. c. 5 seqq.
§ X. " Cum enim qusevis propositio possit converti, modo quan-
titas prssdicati probe observetur, hinc necessario sequitur, quod
quivis Syllogismus, adhibita propositionum conversione, in quavis
figura possit proponi, ex quo non potest non sequalis modorum
444. APPENDIX.
numeriis in unaquaque figiira oriri, licet ilK non ejusdem semper
sint quail titatis.
§ xi. " Operas pretium non est prolixe per omnia Syllogismorum
singulis figuris adscriptorura exempla ire, sufficiat uno assertionem
illustrasse, v. gr. in prima figura, modo Barbara liic occurrit Syllo-
gismus apud d. Autor. c. 5.
0. Sapiens suhjtcitur voluntati Dei,
0. Ilonestus est sajnens,
E. 0. honestus suhjicitur voluntati Dei.
§ xii. " Hunc in secimda figura ita proponere licet :
Quidam, qui suhjicitur voluntati Dei, est omnis sapiens,
Omnis honestus est sapiens,
E. Omnis honestus suhjicitur voluntati Dei,
ratio concludeiidi maiiet eadein, sapiens enim et is qui suhjicitur
voluntati Dei, uniuntur in Majore, dein sapiens et Honestus in
Minore, ergo in conclusione idea sapientis et Ejus qui voluntati
Dei suhjicitur, quoque conveniunt.
§ xiii. " In tertia figura ita se habebit :
0. Sapiens suhjicitur voluntati Dei,
Q. Sapiens est omnis honestus,
E. 0. honestus suhjicitur voluntati Dei,
nec in liac concludendi ratione aliquid desiderari potest, nam me-
dius terminus universaliter unitur cum conclusionis pr?edicato,
deinde, quantum sufficit, conjungitur cum ejusdem subjecto, seu
omni honesto, ergo subjectum et pnedicatum se quoque mutuo
admittent.
§ xiv. " Cseterorum eadem est ratio, quod facile ostendi posset,
nisi tricas illas vel scribere vel legere tsediosum foret. Ex liis
autem sequitur, quod omnes regulce speciales, quce niodis vidgari-
hus attemperatce vulgo circumferuntur,falsce sint, quod sjieciatim
ostendere liceat.
§ XV. " In uiiiversum triplici modo impingitur, vel enim conclu-
sio creditur absurda, qucB talis non est, vel vitiuni est in materia,
ac altera proimissaruni falsa, vel adsunt qiiatuor termini, adeo-
que alisurditas conclusionis, si aliqua subest, nunquam ab ea causa
dependet, quam referunt regulas.
APPENDIX. 44d
§ xvi. " Sed videamus distinctius, (1) major in jprima figura
semper sit univeralis
§ xvii. " Inflectam hue exemplum minus controversum, quod
Autor, Art. Cog. p. 3, c. 7, in modo Disaniis, tertise figurse, pro-
ponit :
Quldam impii in honore hahentur in micndo,
Quidam vituperandi sunt omnes i7npii,
E. quidam vituperandi in honore hahentur in viundo.
§ xviii. " Hie habes primam figuram cum majore partieulari,
optime iterum coneludentem, nam licet medius terminus particu-
lariter sumatur in majore, ejus tamen ille est capacitatis, ut in
eodem convenientia prsedicati et subjecti ostendi queat, et nisi hoc
asset, nee in tertia figura rite coneluderetur.
§ xix. " Nee valde obsunt, quse vulgo illustrandse regules addu-
cuntur. Ex sententia Weis. in Log. p. i., lib. 2, c. 2, § 4, male ita
concluditur :
Q. animal volat,
0. Leo est animal,
E. Q. Leo volat.
Verum si animal sumitur in minore sieut in majore, tum ilia falsa
est, si vero alio sensu, tum existunt quatuor termini ; his ergo
causis, non particularitati Majoris, vitiosa conelusio tribuenda.
§ XX. " Nam alias ita bene concluditur :
Q. animal volat,
0. avis est animal, (illud quoddam),
E. 0. avis volat,
nam licet medius terminus jiarticularis sit, tantae tamen est latitu-
dinis, ut cum utroque Conelusionis termino possit uniri.
§ xxi. " Porro (2) Minor semper sit affirmans. Sed quid desi-
derari potest in hoc Syllogismo :
0. Homo est animal rationale,
Leo non est homo,
E. non est animal rationale ?
et nonne ilia ratio concludendi manifesto bona est, quas subjectum
et prsedicatura, quae in certo tertio non conveniunt, inter se quoque
pugnare contendit ?
§ xxii. " Sed ais, mutemus paululum Syllogismmn et absurditas
conelusionis erit manifesta :
446 APPENDIX.
0. Homo est miimal,
Leo non est homo,
E. Leo non est animal !
Verum si terminus animalis in Conclusione perinde sumitur, sicut
suppositus fiiit in majore, nempe particular iter, turn conclusio est
verissima ; si autem aliter accipiatur, turn evadunt quatuor termini,
quibns adeo, non negationi Minoris, absiirditas conclusionis est
imputanda, qiise observatio in omnibus exemplis quae hie objici
possunt et solent, locum habet.
§ xxviii. " Sed revertamur ad regulas vulgares ! Nimirum (3)
In secunda fi[/ura major sit universalis. Verum cur non ita
liceat concludere :
Quidam dives est Saxo,
Quidam Germanus est omnis Saxo,
E. Quidam Germanus est dives 1
quod argumentum Weis. 1. 2, c. 4, § 2, intuitu tertiee figurae pro-
ponit.
§ xxix. " Argumenta, quae fallere videntur, v. gr. quod Weisius
1. 2, c. 3, § 3, profert :
Quidam homo est sapiens,
JVidlus stulfus est sapiens,
E. Nullus stultus est homo,
et similia, responsione, § 22, data eliduntur ; nimirum conclusio vel
non est absurda, si recte intelligatur, vel adsunt quatuor termini,
quibus adeo, non particularitati majoris, vitium est imputandum.
§ XXX. " Amplius (4) Ex jniris ajirmativis in secunda jigura
nihil concluditur, sed rairum foret, si ilia concludendi ratio falleret,
quae fundamentum omnium Syllogismorum affirmativorum tam
evidenter prae se fert ! Hoc argumentum utique formaliter bonum
est :
Omnis sapiens sua sorte est contentus,
Paidus sua sorte est contentus,
E. Paulus est sapiens.
§ xxxi. " Sed fallunt multa argumenta, v. gr. Weisio d. c. 8, §
3, adductum :
Omnis lepiis vivit,
Tu vivis,
E, Tu es lepus,
APPENDIX, 447
verum non falliint ob affirmationem prflemissariim, sed quia vel
minor falsa est, si scil. prpedicatum accipiatur eodem sensu, quo in
Majore sumtum est, vel quia adsunt quatuor termini, si prsedicatum
Minoris particulariter et alio sensu accipiatur.
§ xxxii. " Non possunt etiam vulgo diffiteri, quin ex puris affir-
mativis aliquando quid sequatur, verum id non v'lformce sed ma-
terice fieri causantur, vide Ulman. Log. 1. 3, c. 3, § 4. Hsec vero
est petitio principii, nam qu?e conveniunt in uno tertio, ilia etiam
inter se convenire debent, idque non fortuito, sed virtute nnionis
laudatae, seu beneficio formse.
§ xxxiv. " In tertia figura (5) Minor semper sit affirmans.
Ego tamen sic recte concludi posse arbitror :
Quoddam laudandum est omnis virtus,
JVuNum hiudanduvi est qucedam magnificentia,
E qucedam magnificentia non est vij-tus.
§ XXXV. " Nee valde urgent exempla opposita Weisius d. 1. 2, c.
4, § 2, hoc affert :
Omnis homo ambulat,
Nidlus homo est porcus,
E. quidavi 2)orcus non ambulat,
nam recurrit responsio § 22 data, quae vel conclusionem falsam
non esse, vel causam falsitatis a quatuor terminis dependere osten-
dit, qu^ etiam locum haberet, licet conclusionem universalem,
Nidlus porcus amhidat, assumas.
§ xxxvi. " Tandem (G) In tertia figura conclusio semper sit
particidaris. Verum Syllogismum cum conclusione universaK,
jam exhibui § 13, in Exemplis autem quae vulgo afiferuntur, v. g7\
Omnis senator est ho7ioratus,
Omnis senator est homo, (quidam sell.),
E. omnis homo est honoratus,
vide Weis. d. 1 2, c. 4, § 3, occurrunt quatuor termini, (nam homo,
in minore particulariter, in conclusione universaliter sumitur), qui
adeo veram absurdse conclusionis causam, ac simul regulse vulgaris
falsitatem ostendunt.
§ xxxvii. " Ilia autem omnia, quse contra vulgares regulas
hactenus disputavimus, non eo pertinent, quasi rationem conclu-
44-8 APPENDIX,
dendi rejiciendis regulis liinc iiide coiifectam commendemus, ita
ut in demonstrationibiis eadem iiti, aut valde delectari debeamus.
Quin omni potius eo spectaiit, ut Peripateticos, qui formani Syllo-
gismorum essentialem vel omnino non vel nimis frigide exponunt,
in explicandis etiani eorum figuris accidentalibus, falli probarem.
§ xxxix. " Atque ex hactenus dictis etiam intelligi potest, quae
nostra de Reductione sit sententia. Nimirum ex nostris hypothe-
sibus ilia nihil aliiid est, quam SijUogismorum 'per omnes quatiior
fignras accidentales, salva semper conclusione, facta variatio.
§ xl. " Pertinet igitur ilia tantum ad Frcemissa, Syllogismus
enim semper ut instrmnentuni veritatis inquii-endae considerari,
adeoque queestio probanda, qua3 semper immobilis sit, nee, prout
visum est, varietur, prjesupponi debet.
§ xli. " Keductionis unica Lex est, ut simpliciter, juxta figuroa
indolem, propositiones convertamus, quod sine ulla dijSicultate pro-
cedit, dummodo quantitatem subjecti et prsedicati debite confidere-
mus, ceu ex iis quae de Conversione diximus satis liquet.
§ xlii. " Finis est, ut per ejusmodi variationem, terminorum
unionem vel separationem eo accuratius intelligamus, hinc omnis
utilitas reductioni non est abjudicanda, si enim recte instituatur,
ingenium quantitati propositionum observandce magis magisque
assuescit, ac inde etiam in penitiorem format esseutialis intelligen-
tiam provehitur.
§ xliii. "In vuhjari i?efZ((C^io?ie, qu^e in libellis logicis passim
exponitur, vide Aut. Art. Cog. p. 3, c. 9, quasdam exempla repre-
liendi non debent, quando v. g. Gesare ad Gelarent reducitur, nam
ibi simplici conversione alicujus propositionis defunguntur, juxta
legem, quam § 41, reductioni dedimus.
§ xliv. " Sed si ab illis exemplis abeas, parura vel nihil est,
quod in eadem laudari debeat, dum fere ex falsis liypothesibus
omnis reductio oritur, nam conversio p>Gr contrapositionem pras-
supponitur, quam tamen valde dubiam esse, supra ostendimus,
praeterea peculiares modi in singidis figuris adstruuntur, ac omnis
reductio ad p>rimam figuram facienda, esse existimatur, cum tamen
idem Syllogismus per omnes figuras variari queat.
§ xlv. " Ipsa vero reductio nullis legibus adstricta est, converti-
tur Conclusio, transponuntur Prremissje, propositiones negativte
mutantur in affirmativas, atque ita quidvis tentatur, modo figura
APPENDIX. 449
intenta obtineatur. Quo ipso puerilis error, quo Logica, pro arte
concinnandi tres lineas, easque in varias formas mutandi habetur
satis elucet. luepta scientia est, quoe in verbis disponendis, circum-
agendis aut torquendis unice, occupatur.
§ xlvi. " Juxta haec igitur, vulgar! modo reducere, maximam
partem nihil aliud est, quam errorem errore tegere, ingenia discen-
tium torquere, ac magno conatu magnas nugas agere, inscitiamque
professa opera ostendere." — Ed.]
D. SYLLOGISTIC MOODS.
(Vol. I. p. 401.)
(a) Direct and Indieect Moods.
(1) Theie Principle. — First and Fourth Figure.
(See above, Vol. I, p. 423.)
Direct and Indirect Moods, — principle of. — That the two terms
should hold the same relation to each other in the conclusion, that
they generally hold to the middle term in the premises. This de-
termined by the Question. This constitutes direct, immediate,
natural, orderly inference. When reversed, by Conversion, there
emerges indirect, mediate, unnatural, irregular inference.
In the two last Figures, (Second and Third), the two terms hold
the same relation to the middle term in the premises ; ergo no
indirect inference, but always two direct conclusions possible.
In the first Figure, as the two terms are subordinated to each
other in the premises, one direct conclusion from premises,
whether read in Extension or Comprehension, and, consequently,
an indirect one also, — the First Figure being first figure in Exten-
sive quantity ; the Fourth Figure being first figure in Comprehen-
sive quantity. Direct and indirect moods in each.
1. Blunder about definition of major and mmor terms by logi-
cians, (for which Aristotle not responsible)," cause of fancy of a
Fourth Figure, constituted by indirect moods in comprehension.
2. That predicate could have no prefinition, and, therefore, though
ci.'&ee^iah\,[NotcB etAnimadversiones tographo edttce cura Caspari Posneri
in Compendium Dialecticum T). Conradi Prof. Pub. Jena;. 1656, Ad. L. iii. c.
Horneii, nunc primum ex Auctoris An- viii.]
VOL. II. 2 F
450 APPENDIX.
they allowed its converse, the direct inference was not suffered.
This in Fapesmo, Frisesmo, (these alone, by some logicians, ad-
mitted in the First Figure), and Fesapo and Fresison in Fourth or
Comprehensive First, a
3. That major proposition, that which is placed first.
Fourth Figure. — The First Figure, and that alone, is capable of
being enounced in two orders, those of Breadth and of Depth. It
is exactly the same syllogism in either order ; and, while the order of
Depth was usually employed by the Greeks, Orientals, and older
Latins, that of Breadth has been the common, if not the exclusive,
mode of enouncement among the western logicians, since the time
of Boethius. In either form, there are thus four direct moods,
and five indirect, — in all nine moods ; and if the Figure be held to
comprise the moods of either form, it will have eighteen moods, as
in fact is allowed by some logicians, and, among others, by Men-
doza, (Disj). Log. et Met. T. I. pp. 515, 516), Martianus Capella,
{De Septem Artihus Liber alihiis, L. iv., De Dialectica, in cap.
Quid sit Prcedicativus Syllogismus, (see above, p. 424), states
and allows either form, but, like his contemporaries, Greek and
Latin, he employs in his examples the order of Depth.
Now, mark the cajDrice of the logicians of the west subsequent
to Boethius. Overlooking entirely the four direct moods in the
order of Depth, which they did not employ, as the conclusion
would, in these cases, have been opposed to their own order ; they
seized upon the five indirect moods of the order of Depth, as this
afforded a conclusion corresponding to their own, and constituted
it, thus limited, into a Fourth Figure.
Did not make two forms of First Figure.
An indirect conclusion is in subject and predicate the reverse of
a direct ; opposed, therefore, to the order of predication marked
out by the premises which the direct conclusion exclusively follows.
a [That foui-thFigui-e differs from first § 3, p. 29. Campanella, Phil. Sat.
only by transposition of Premises,— held Dialect., Lib. ii. c. vi. art. xi. p. 391,
by Derodon, Loyica Restituta, p. 606. and art. iv. p 385, (1635). Ridiger, De
Camerarius, Disputationes Philosophicce, Sensu Veri et Falsi, ii. 6, § 36. Criisius,
Disp. i., qu. 13, p. 116. Caramuel, Rat. Weg Zur Geicissheit, § 335, p. 606. Plat-
ed Real. Phil., Disp. xii. p. 45. Ircnasus, ner, Philosophische Aphorismen, i. § 554,
Iitte/j. Phil., Ehnienta Lor/!re.i, Sect. iii. p. 267.]
APPENDIX.
451
An indirect conclusion, (what the logicians have not observed)," is
an inference from the dkect conclusion, and, therefore, one mediate
from the premises.
(2) Moods of Fourth Figure redressed.
(Early Pajier — previous to 1844. Later signs of quantity sub-
stituted. — Ed.)
I. Bamalip, — only Barbara with transposed premises and con-
verted couclu.sion.
(2) All irons are (some) metals ;
(1) All metals are (some) minerals ;
All irons are {some) minerals.
(By conversion.)
Some minerals are (all) irons.
(Minerals) ,
■ : (Metals) ,
(Redressed)
: (Irons).
II. Calemes, — only Celarent with transposed premises and con-
verted conclusion.
(2) All snails are (some) mollusca ;
(1) No molluscum is any insect ;
No snail is any insect.
(By conversion)
No insect is any snail.
(Insect) :
; (Molluscum) , m : (Snail)
(Redressed)
III. Dimatis, — only Darii with transposed premises and con-
verted conclusion.
« But see Contarenus, De Quarta Figura Syllog., Opera, p. 235. — Ed.
452
APPENDIX.
(2) Some stars are {some or all) planets ;
(1) All jjlanets are some things moving round sun
Some stars are sotne things moviny round sun ;
(By conversion)
Some things moving round sun are some stars.
{Moving round Sun),
: {Planets) : ,
(Redressed)
, {Stars)
IV. Fesapo, [Felapos]."
(2) iVo ai-tery is any vein ;
(l) All veins are {some) bloodvessels
No artery is {some) bloodvessel.
(By conversion)
Some bloodvessel is no artery.
{Bloodvessels) ,
M : ( Vei7i) : -
(Redressed)
: (.1 rfery)
V. Fresison, [Frelilos].
(2) No muscle is any nerve ;
(1) Some nerves are {some) expansion on hand
No muscle is {some) expansion on hand.
(By conversion)
Some expansion on hand is no muscle.
^ Zabarella, Opera Logica, Be Quarta verses premises and reduces to Fapesmo
Fig. Syll, pp. 118,119,125. Burgers- an indirect mood of First; thusviolat-
dyk, Instit. Lor/., L. ii. c. 7, p. 167, re- ing the rule of that Figure.
APPENDIX. 453
{Expansion mi hand), m , (N'erve) : | m : {Muscle)
(Redressed)
(March 1846.) — My universal law of Figured Syllogism excludes
the Fourth Figure. — What worse relation of subject and jwedicate
subsists between either of tiuo terms and a common third term
with which one, at least, is positively related ; that relation sub-
sists between the two terms themselves. What relation, &c. ; that
relation, &c. Now, in Fourth Figure, this is violated ; for the predi-
cate and subject notions, relative to the middle term in the pre-
mises, are in the conclusion turned severally into their opposites
by relation to each other. This cannot, however, in fact be ; and,
in reality, there is a silently suppressed conclusion, from which
there is only given the converse, but the conversion itself ignored.
Fourth Figure. Reasons against —
1°, Could never directly, naturally, reach (a) Conclusion from pre-
mise, or (b) Premises from quresitum.
2", All other figures conversion of premises of First, but, by
conversion of conclusion, (as it is), no new figure.
3°, All other figures have one conclusion Fom-th a converted
one, often dijBFerent.
(March 1850.) — Fourth Figure. The logicians who attempt to
show the perversion in this figure, by speaking of higher and
lower notions, are extra-logical. Logic knows nothing of higher
and lower out of its own terms ; and any notion may be subject
or predicate of any other by the restriction of its extension.
Logic must show the perversion in this Figure ex facie syllogismi,
or it must stand good. On true reason, why no Fourth Figure,
see Ai-istotle, Anal. Pr., L. i., c. 23, § 8, and Pacius, in Commen-
tary.
(March 1850.) — Fesapo and Fresiso, (also Fapesmo, Frisesmo),
proceed on the immediate inference, unnoticed by logicians, that
the quantities, apart from the terms, may, in propositions InA and
AnI, be converted.
454? APPENDIX.
Averroes on Prior Analytics, B. i., Ch. 8.
" If we ask whether A be in C, and say that A is in C, because
A is in B, and B in C ; in this case, there is a natural syllogism
by general confession ; and this in the First Figure.
" In like manner, if we say that A is not in C, because B is in
C, and B is not in A ; it is plain that we collect that conclusion by
natural process ; and this is the Second Figure, which is frequently
found employed by men in their ordinary discourse.
" In like manner, also, if we say that A is in C, because A and C
are in B ; that syllogism is also natural to us, and is the Third
Figure. But if we say A is in C, because C is in B, and B in A ;
the reasoning is one which no one would naturally make ; for the
reason that the quajsitum, (that is, C to be in A), does not hence
follow, — the process being that in which we say A is in C, since A
is in B, and B in C ; and this is something which thought would
not perform, unless in opposition to nature. From this it is mani-
fest, that the Fourth Figure, of which Galen makes mention, is not
a syllogism on which thought would naturally light," (&c.) There-
after follows a digression against this figure. See also the same
book, Ch. 23d, and the Epitome, by Averroes, of the same, Ch. i.
(3) Fourth Figure. — Authorities for and against.
Admitted by —
Ildefonsus de Penafiel, Cursus Philosophicus, Disp. Summul.
D. iii. p. 89. G. Camerarius, Disput. Philos., P. i., q. xiii., p. 116.
Po7't B.oyal Logic, p. iii. c. 8, and c. 4. Ridiger, De Sensu Vei'i et
Falsi, L. ii., c. 6, § 36. Hauschius in Acta JErud. p. 470 ct seq.
Lips. 1728. 'Noldms, Logica Recognita, c. xii. p. 277. Crakan-
thorpe, Logica, L. iii. c. xv. p. 194, (omitted, but defended).
Lambert, JS^eues Organon, I. § 237, et seq. Hoffbauer, Analytik
der Urtheile und Schliisse, § 138. Twesten, Logik, inshesondere
die Analytik, § 110. Leibnitz, Opera, ii. 357; v. 405 ; vi. 216,
217, ed. Dutens. Oddus de Oddis, (v. Contarenus, Non Pari
Quart. Fig. SylL, Opera Omnia, p. 233, ed. Venet, 1589.)
Eejected by —
Averroes, In. An. Prior., L. i. c. 8. Zabarella, Opera Logica,
De Quarta Fig. SylL, p. 102 et seq. Purchot, Instit. Phil. T. I.
Log. P. iii. c. iii. p. 169. Molinaeus, Flementa Logica, L. i.
c. viii. Facciolati, Rudinienta Logica, P. iii. c. iii. p. 85. Scay-
APPENDIX.
455
nus, Paraphrasis in Organ., p. 574. Timpler, Logicce Systema,
L. iv, c. i. qii. 13, p. 543. Platner, Philosophische Aphorismen,
I. p. 267. Burgersdicius, Instit. Log. L. ii. c. vii. p. 165. Dero-
don, Logica Restituta, p. 606. Wolf, Phil. Rat, § 343, et seq.
(Ignored.) Hollmann, Logica, § 453, p. 569. Goclenius, Pi^o-
hlemata Logica, P, iv., p. 119. Keckermann, Opera, T. I., Syst.
Log. Lib. iii., c. 4, p. 745. Ai'riaga, Cursus Philosophicus, In
Summulas, D. iii. § 5, p. 24. Aristotle, An. Prior, i. c. 23,
§ 8 ; c. 30, § 1, (omitted). Jo. Picus Miraudulanus, Conclusiones,
Opera, p. 88. Melanchthon, in 1st edition of Dialectic, L. iii.,
De Figuratione, (1520), afterwards (1547), restored, (Heumanni,
Acta, iii. 753). Cardinalis Caspar Contarenus, Epistola ad Oddum
de Oddis, De Quart. Fig. SylL Opera, p. 233 (1st ed., 1571).
Trendelenburg, Elementa Logica, § 28, &c. Herbart, Lehrbiich
der Logik, Einleit., 3, § 71. Hegel, Encyclopcedie, § 187. Pries,
System der Logik, § 57 b. Griepenkerl, Lehrbuch der Logik, §
29 et seq. Drobisch, Logik, § 77, p. 70. Wallis, Institutio Logicce,
L. iii. c. ix. p. 179.
(6) INDIKECT MOODS OF SECOND AND THIRD FIGUEES.a
From
(II.
Fig.)
i.
/Cesare
^Cumestres
Reflexim ; (1, 2, 5, 8, 9) p, Cesares.
ii.
Reflexim ; (2, 5, 8, 9.) Camestre, Ca-
mestres, Faresmo, (only subaltern of
Camestres) ; rejected (2), admitted
(3, 6.)
iii.
Festino
Premises reversed ; (2, 3, 4, 5, 6, 7, 8, 9.)
Firesmo, Frigeros,
iv.
Baroco
Premises reversed ; (2, 5, 7, 8, 9.) Bo-
cardo, Moracos, Forameno.
(III.
Fig.)
i.
Darapti
Reflexim; (1, 2, 3, 4, 10, 11.)
ii.
Felaptou
Premises transposed ; (4, 5, 6, 7, 8, 9,
11.) Fapemo, Fapelmos.
iii.
/Disamis
\Datisi
Reflexim; (4, 7, 10, 11.)
iv.
Reflexim ; (4, 7, 10, 11.)
V.
Bocardo
Premises transposed ; (4, 7, 9, 11.) Ba-
roco, Macopos, Danorcoc.
vi.
Ferison
Premises transposed ; (4, 5, 6, 7, 8, 9,
11.) Frisemo, Fiseros.
a The indirect Moods of the First to the authorities given on following
Figure are universally admitted. page. — Ed.
/8 The numbers within brackets refer
456
APPENDIX.
(TI. Fig.)
Mart. Capella
Duns Scotus
3. Lovaniciises, (1535)
4. ! Pacius, (1584)
Conimbricenses
9.
10.
11.
Burgersdicius, (1626)
Caramuel, (1642)
Scheibler, (1653)
Noldius, (1666)
Cesare, reflexim.
Cesare and Camestres, conclusions simp-
ly converted ; Festino and Baroco.
Rejects (and rightly), what has since
been called Faresmo, as a mere sub-
altern of Camestres {An. Pr. L. i. qu.
23. See also Conimbricenses, In
Arist.Dial. II. p. 362.)
Faresmo, Firesmo.
Firesmo (oa An. Pv. L. i. c. 7, and rela-
tive place of his Com. Anal.)
Record that indirect moods from Cesare
and Camestres ; and also Friseso, Bo-
cardo were admitted by some " re-
centiores" (II. p. 362.)
Faresmo, Firesmo.
Moracos, Frigesos.
Cesares, Camestres, Firesmo, Bocardo.
Cesares, Camestre, Firesmo, Forameno ;
(he has for the direct mood Facrono,
in place of Baroco.)
(III. Fig.)
Apuleius
Cassiodorus
Isodorus
Duns Scotus
Lovanienses
Pacius
Conimbricenses
Burgersdicius
Caramuel
Scheibler
Noldius
Darapti, reflexim.
Do.
Do.
Darapti, Disamis, and Datisi, their con-
clusions simply converted; Felapton,
Bocardo, Ferisou, {Sup. An. Pr., L.
i. qu. 24.)
Fapemo, Frisemo (ib.)
Fapemo, Frisemo (ib.)
Record that some " recentiores" admit
indirect moods from Darapti, Disa-
mis, Datisi ; also Fapesmo, Frisesmo,
and Baroco.
Fapemo, Frisemo.
Fapelmos, Macopos, Fiseros.
Admits them from Disamis, Datisi, Da-
rapti, but not from those which con-
clude particular negations.
Danorcoc, (he has for Bocardo Docam-
roc), Frisemo, Fapemo, and what are
converted from Darapti, Disamis, and
Datisi without names.
Darapti virtually two moods ; this
maintained by Theophrastus.
APPENDIX.
457
Indirect moods are impossible in the Second and Third Figures,
for what are called indirect conclusions are only the direct conclu-
sions. Mem., that in the Second Cesare and Camestres are vir-
tually one ; whilst in the Third Figure Darapti is virtually two, as
Disamis and Datisi are one.
For the particular quantification of the Predicate, useful illus-
trations, as in the First from Fapesmo, Frisesmo, or (in the pseudo
Fourth) from Fesapo and Fresiso ; so in the Second Figure from
what have been called the indirect moods of Figure II.
1. Bocardo.
2. Firesmo.
1. Baroco.
2. Fapemo.
2. Frisemo.
(1853.) Blunders of Logicians. — What have been called the
Indirect Moods of the Second and Third Figures, arise only from
the erroneously supposed transposition of the premises ; and the
Fourth Figure is made up of the really indirect moods of the First
Figure, with the premises transposed.
(c) New Moods — Notes upon Table of Syllogisms-o
Fig. I. vi. — Corvinus, {Institution es Philosophice Rationalis,
1742, § 540), says : — " There sometimes appears to be an inference
from pure particulars. For example, Soinie learned are [_some']
ambitious men ; some men are [all the] learned ; therefore, some
a See below, Appendix xi. — Ed.
458 APPENDIX.
men are ambitious. But the minor proposition, althougli formally
particular, involves, however, a universal, to wit, its converse, — All
the learned are[^some^ men, — which is equipollent." — Why not, then,
scientifically enounce, (as I have done), without conversion, what
the thought of the convertend already really and vulgarly involved?
In all Figures. — I have been not undoubtful, whether the
syllogisms of the class, in which the two premises, being the
same, are mutually interchangeable, should be regarded as a single
or as a double mood. Abstractly considered from all matter, the
mood is single ; for the two premises, however arranged, afford
only a repetition of the same form. But so soon as the form is
applied to any matter, be it even of a symbolical abstraction, the
distinction of a double mood emerges, in the possible interchange
of the now two distinguished premises. To the logicians this ques-
tion was only presented in the case of Darapti (III. ii.) ; and on this
they were divided. Aristotle [An. Pr. i. c. 6, § 6) contemplates
only one mood ; but his successor, Theophrastus, admitted two,
(Apuleius, De Hah. Doctr. Platonis, L. iii. OjJ. p. 38, Elm). Aris-
totle's opinion was overtly preferred by Alexander, {ad locum, £ 30,
ed. Aid. quoted above, p. 419), and by Apuleius, [1. c.) ; whilst that
of Theophrastus was adopted by Porphyry, in his lost connnentary
on the Prior Analytics, and, though not without hesitation, by
Boethius, (De Syll. Gateg. L. ii.. Op. pp. 594,598, 601, 604). The
other Greek and Eoraan logicians silently follow the master; from
whom, in more modern times, Valla (to say nothing of others) only
differs, to reduce, on the counter-extreme, Cesare and Camestres,
(II. ix. a, and X. b), and, he might have added, Disamis and Datisi,
(III. iv. v.), to a single mood, [De Dial., L. ii. c. 51). (For the ob-
servations of the Aphrodisian, see above p. 415 et seq.)
To me it appears, on reflection, right to allow in Darapti only a
single mood ; because a second, simply arising through a first, and
through a transposition, has, therefore, merely a secondary, cor-
relative, and dependent existence. In this respect all is differ-
ent with Cesare and Camestres, Disamis, and Datisi. The prin-
ciple here applies in my doctrine to the whole class of syllogisms
with balanced middle and extremes.
Fig. II. xii. b. — David Derodon, [Log. Rest. De Arg., c. ii. § 51),
APPENDIX. 459
in canvassing the special rule of the Second Figure, — that the
major premise should be universal, — he now approbates, he now
reprobates syllogisms of this mood ; but wrong on both alterna-
tives, for his admissions and rejections are equally erroneous. " Hie
syllogismus non valet; — Aliquod animal est [aliquod^ rationale ;
sed [idlus] asinus non est [idlus^_^ rationalis ; ergo, [uUus] asinus,
non est [aliquod] animal." (P. 63.5.) The syllogism is valid ; only
it involves a principle which Derodon, with the logicians, would
not allow, — That in negatives the predicate could be particular, —
(see Log. Rest. De Argument, c. ii. § 28, p. 623.) Yet almost
immediately thereafter, in assailing the rule, he says : — " At multi
dantur syllogismi constantes majori particular!, qui tamen sunt
recti; ut, — Aliquod animal non est [idlus'] lapis; sed [omnis]
adamas est [aliquis] lajns; ergo, \idlus] adamas non est [aliquod]
animal." (This syllogism is, indeed, II. iii. a ; but he goes on :)
"Item: Aliquod animal est [aliquod] rationale; sed [idlus]
lapis non est [tdhis] rationalis ; ergo [ullus] lapis non est [ali-
quod] animal." Now these two syllogisms are both bad, as in-
ferring what Derodon thinks they do infer, — a negative conclusion
with, of course, a distributed predicate, (p. 623) ; are both good,
as inferring what I suppose them to infer, — a negative conclusion
Avith an undistributed predicate.
Fig. III. viii. b. — Derodon, {Ibid, § 54), in considermg the
Special Rule of the Third Figure, — that the minor premise should
be affirmative, — alleges the following syllogism as "ritious:" —
"Omnis homo est [aliquod] animal; sed [tdlus] homo non est
[ullus] asinus; ergo, [ullus] asinus non est [aliquod] animal,"
(p. 638.) It is a virtuous syllogism, — with a particular predicate
(and not a universal, as one logician imagines), in a negative con-
clusion. — Again, (omitting his reasoning, which is inept), he pro-
ceeds : — " Hie vero syllogismus non est vitiosus, sed rectus : —
[Omnis] homo est [quidam] rationalis ; sed [ullus] homo non est
[ullus] asinus [or Deus] ; ergo [ullus] asinus [or Deus] non est
[quidam] rationalis." This syllogism is indeed correct ; but not,
as Derodon would have it, with a distributed predicate in the con-
clusion. That his conclusion is only true of the asinus, per acci-
dens, is shown by the substitution of the term Deus; this showing
his iUation to be formally absurd.
460 APPENDIX.
Fig. III. ii. — Derodon {Ibid.) says : — " Denique, conclusionem
in tertia figura debere esse particularem, non imiversalem, sta-
tuunt commimiter Philosophi ; unde hie syllogismus non valet ;
— ' Omnis homo est [quidanij rationalis ; sed omnis homo est
[quoddaml animal; ergo, omne [quoddam'] animal est [quoddam]
7'ationale. Verum, licet conclusio sit universalis, syllogismus
erit bonus, modo," &c., (p. 638.) The syllogism is, and must
remain, vitious, if the subject and predicate of the conclusion be
taken universally, whilst both are undistributed in the antecedent.
But if taken, as they ought to be, in the conclusion, particularly,
the syllogism is good. Derodon, in his remarks, partly overlooks,
partly mistakes, the vice.
Derodon, criticising the Special Eule of the First Figure, — that
the major premise should be universal, — says, inter alia : — " At
multi dantur syllogismi primre figure constantes majori particu-
lari, qui tamen sunt recti : ut, — ' Aliquod animal est [aliquod^
rationale; sed homo est [aliquod^ animal; ergo [!!] homo est
aliquis] rationalis': item," &c., &c., (p. 627.) This syllogism is
vicious ; the middle term, animal, being particular in both its
quantifications, affords no inference.*
XI.
LOGICAL NOTATION.
(See Vol. I., p. 305.)
(a) Lambert's Linear Notation.^
This very defective, — indeed almost as bad as possible. It has
accordingly remained unemployed by subsequent logicians ; and
although I think linear diagrams do afford the best geometrical
illustration of logical forms, I have found it necessary to adopt a
a See above, p. 317. — Ed. bert and Eulcr, see S. Maimon, Versuch
$ For Lambert's scheme of notation, einer neiten Logih, Sect, iv., § 7, p. 64 ct
see bis Neiies Organon, I. § 21. ; and seq, Berlin, 1794. — Ed.
fur a criticism of the schemes of Lam-
APPENDIX. 461
method opposite to Lambert's, in all that is peculiar to him. I
have been unable to adopt, unable to improve, anything.
1°. Indefinite or particular notions can only be represented by
the relation of two lines, and in two ways : 1°, One being greater
than the other ; 2°, One being partially out of relation to the
other. Instead of this, Lambert professes to paint particularity by
a dotted line, i. e., a line different by an accidental quality, not
by an essential relation. But not even to this can he adhere, for
the same notion, the same line, in different relations, is at once
Tiniversal and particular. Accordingly, in Lambert's notation, the
relation of particular notions is represented sometimes by a conti-
nuous, sometimes by a dotted, line, or not represented at all. (See
below, I* 1, 2,3, 4, 5).
2°, The inconsistency is seen at all climax in the case of the
predicate in affirmatives, where that term is particular. In Lam-
bert's notation it, however, shows in general as distributed or uni-
versal ; but in this he has no constancy. (See 1*, 1, 2, 3, 4). But
the case is even more absurd in negative propositions, where the
predicate is really taken in its whole extent, and yet is, by the
dotted line, determinately marked as particular. (See 4).
3°, The relation of negativity, or exclusion, is professedly re-
presented by Lambert in one line beyond, or at the side of, another.
This requires room, and is clumsy, but is not positively erroneous :
— it does express exclusion. But his affirmative propositions are
denoted by two unconnected lines, one below the other. This is
positively wrong ; for here the notions are equally out of each
other as in the lateral collocation. But even in this he is incon-
sistent ; for he as often expresses the relation of negativity by
lines in the relation of higher and lower. (See below, 1, 4).
4°, He attempts to indicate the essential relation of the lines by
the fortuitous annexation of letters, the mystery of which I have
never fathomed.
5°, He has no order in the relation of his lines.
The middle term is not always the middle line, and there is no
order between the extremes.
This could not indeed be from his method of notation ; and ex-
cept it be explained by the affixed letters, no one could discover
in his lines the three compared notions in a syllogism, or guess at
the conclusion inferred. (See 1 — 5).
462 APPENDIX.
6°, From poverty the same diagram is employed to denote the
most different moods in affirmative and negative. (Compare 2
and 3 with 4).
7°, No order in the terms in the same figure.
8°, Incomplete. Lambert can represent ultra-total, &c., included
in affirmative, but not ultra-total, excluded in negative. Has the
merit of noticing this relation.
9", Lambert ; but it is needless to proceed. What has been
already said, shows that Lambert's scheme of linear notation is, in
its parts, a failure, being only a corruption of the good, and a
blundering and incongruous jumble of the natural and conven-
tional. The only marvel is, how so able a mathematician should
have propounded two such worthless mathematical metliods. But
Lambert's geometrical is worse even than algebraic notation.
To vindicate what I have said, it will be enough to quote his
notation of the moods of the Third Figure, (I. p. 133), which I
shall number for the previous references.
1.* Darapti.
1. Felapton.
2. Disamis.
3. Datisi.
4. Bocardo.
5. Ferison.
HI. F
IGUKE.
. C-
■ c
M
Ill
. B—
1)
M
m
0-
c
B-
b
B-
b
M
. . C .
m
C-
M
. B . .
c
111
B-
—
b
M
C . . .
in
M-
— mC
B . . .
— -
— c
APPENDIX. 4(53
(h) Notation by Maass.
Professor Maass of Halle « discontented, not unreasonably, with
the geometrical notations of Lambert and Euler, has himself pro-
posed another, compared with which, those of his predecessors
show as absolutely perfect. It will be sufficient to despatch this
scheme, with a very few remarks. To use it is wholly impossible ;
and even the ingenious author himself has stated it towards the
conclusion of his Logic (§ 49o — 512), in the course of which, it is
not, (if I recollect aright), honoured with a single reference. It is
however, curious, as the only attempt made to illustrate Logic,
not by the relations of geometrical quantities, but by the relations
of geometrical relations, — angles.
1°. It is fundamentally wi'ong in principle. For example,
Maass proposes to represent coinclusive notions, notions, there-
fore, to be thought as the same, by the angles of a triangle, which
.cannot possibly be imaged as united, for surely the identity of the
concepts, triangle, trilateral, and figure with angles equal to two
right angles, is not illumined by awarding each to a separate
corner of the figure. On the contrary, coexclusive notions he
represents by angles in similar triangles, and these can easily be
conceived as superposed. The same may be said of co-ordinates.
But, waving the objection that the difierent angles of a figure, as
necessarily thought out of each other, are incapable of typifying,
by their coincidence, notions to be thought as coinclusive, — it is
further evident, that the angles of an equilateral triangle cannot
naturally denote reciprocal or wholly identical notions, in contrast
to others partially identical ; for every angle of every triangle
infers, — necessitates, — contains, if you will, — the whole of every
other, equally as do the several angles of an equilateral triangle.
2°. But Maass is not consistent. He gives, for instance, a tri-
angle, (Fig. 12), to illustrate the subordination of one notion to
another ; and yet he represents the lower or contained notion by
an obtuser, the higher or containing notion by an acuter, angle.
3°. The scheme is unmanifest, — in fact, nothing can be less ob-
trusive. It illustrates the obscure by the obscure, or, rather, it
« Oriindriss der Lor/llc, 1793. I quote ing in the way I do of Maass' scheme of
from the fourth edition, 1823. I regret notation ; for his Logicis one of the best
the necessity imposed on me of speak- compends published even in Germany.
4G4- APPENDIX.
obscures the clear. Requiring itself a painful study to compre-
hend its import, (if comprehended it be) ; instead of informing the
understanding through the eye, it at best only addresses the eye
through the understanding. Difficult, — we only regret that it had
not been impossible.
4°. It is clumsy, operose, complex, and superfluous. Por, to re-
present a notion denoted by a single angle, it is compelled to give
the redundance of a whole triangle ; and three repugnant notions
demand an apparatus of three several figures, and six vacant
angles. In fact, the only manifestation to which this scheme of
angles can pretend, is borrowed from the scheme of figures which
it proposes to supersede.
5°. It is wholly dependent upon the accidents of foreign aid.
To let it work at all, it calls in to its assistance an indefinite plu-
rality of figures, a Greek and Latin alphabet, combinations of let-
ters straight and defiected, and an assortment of lines, thick and
thin, plain and dotted. I have counted one diagram of the
eighteen, and find that it is brought to bear through three varie-
ties of line, four triangles, and eleven letters.
It is needless to enumerate its other faults, its deficiences, ex-
cesses, ambiguities, &c. ; transeat in pace.
(c) The Author's Notation. — No. I. Lineae.
The notation previously spoken of,« represents every various
syllogism in all the accidents of its external form. But as the
number of Moods in Syllogisms Analytic and Synthetic, Intensive
and Extensive, Unfigured and Figured, (and of this in all the
figures,) are the same ; and as a reasoning, essentially identical,
may be carried through the same numerical mood, in every genus
and species of syllogism : it seems, as we should wish it, that
there must be possible also, a notation precisely manifesting the
modal process, in all its essential diff"erences, but, at the same
time, in its internal identity, abstract from every accidental variety
of external form. The anticipation and wish are realised ; and
realised with the utmost clearness and simplicity, in a notation
which fulfils, and alone fulfils, these conditions. This notation
I have long employed : and the two following are specimens.
« See Tabular Scheme at the end of the present volume. — Ed.
APPENDIX. 465
Herein, four common lines are all the requisites : three (horizon-
tal) to denote the terms ; one (two ? — perpendicular) or the want
of it, at the commencement of comparison, to express the quality
of affirmation or of negation ; whilst quantity is marked by the
relative length of a terminal line within, and its indefinite excur-
rence before, the limit of comparison. This notation can repre-
sent equally total and ultra-total distribution, in simple Syllogism
and in Sorites ; it shows, at a glance, the competence or incompe-
tence of any conclusion ; and every one can easily evolve it.
C
M
r "
}
c
]\I
r
Of these : the former, with its converse, includes, Darii, Dabi-
tis, Datisi, Disamis, Dimaris, &c. ; whilst the latter, with its con-
verse, includes Celarent, Cesare, Celanes, Camestres, Cameles,
&c. But of these, those which are represented by the same dia-
gram are, though in different figures, formally, the same mood.
For in this scheme, moods of the thirty-six each has its peculiar
diagram ; whereas, in all the other geometrical schemes hitherto
proposed, (whether by lines, angles, triangles, squares, parallelo-
grams, or circles), the same (complex) diagram is necessarily
employed to represent an indefinite plurality of moods. These
schemes thus tend rather to complicate, than to explicate, — rather
to darken, than to clear up. The principle of this notation may
be realised in various forms."
The problem, in general, is to manifest by the differences and
relations of geometrical quantities, (lines or figures), the differences
and relations of logical forms. The comparative excellence of any
scheme in solution of this problem will be in proportion as it is,
r. Easy; 2°, Simple; 3°, Compendious; 4°, All-sufficient; 5°,
Consistent ; 6°, Manifest ; 7°, Precise ; 8°, Complete.
In the scheme proposed by me,
a Reprinted from Discussions, p. 657. tions denoted by the diagi-ams, see
For a further explanation of the rela- above, vol. i. p. 189. — Ed.
VOL. II. 2 G
4^06 APPENDIX.
1". I denote terms or notions by straight lines ; and, as a syllo-
gism is constituted by three related notions, it will, of course, be
represented by three related lines,
2°. I indicate the correlation of notions by the order and par-
allel coextension of lines. (The perpendicular order and horizon-
tal extension, here adopted, is arbitrary.)
3°. Lines, like notions, are only immediately related to those
with which they stand in proximity. Hence, the intermediate
line in our diagram, representing the middle term of a syllogism,
is in direct relation with the lines, representing the extremes,
whereas the latter are only in mutual correlation through it.
4°. The relative quantity of notions is expressed by the com-
parative length of the related lines. In so far as a line com-
mences, (here on the left), before another, it is out of relation with
it, — is indefinite and unknown. Where a line terminates under
relation, (here towards the right), it ceases absolutely to be. A line,
beginning and ending in relation, indicates a whole notion. A
line, beginning before or ending after its correlative, indicates the
part of a notion.
5°. The kinds of correlation, Affirmation and Negation, are
shown by the connection, or non-connection, of the lines, (here
from the left). The connection, (here a perpendicular line), indi-
cates the identity, or coinclusion, of the connected terms ; the
absence of this denotes the opposite. The lines in positive or affirma-
tive relation are supposed capable of being slid into each other.
This geometric scheme seems to recommend itself by all the
virtues of such a representation, and thus stands favourably con-
trasted with any other. Por it is easy, — simjjle, — compendious, —
all-sufficient, — consistent, — manifest, — precise, — complete.
1°, Easy. — Linear diagrams are more easily and rapidly drawn
than those of figure ; and the lines in this scheme require, in fact,
no symbols at all to mark the terminal differences, far less the
double letterings found necessary by Lambert.
2°, Simple. — Lines denote the quantity and correlation of
notions far more simply than do any geometric figures. In those
there is nothing redundant ; all is significant.
8", Compendious. — In this respect lines, as is evident, are far
preferable to figures ; but Lambert's linear scheme requires more
than double the space sufficient for that here proposed.
APPENDIX. 467
4°, All-sufficieut. — Any scheme by figures, and Lambert's
scheme by lines, is, in itself, unintelligible ; and depends on the
annexation of accidental symbols, to enable it to mark out the
differences and relations of terms. Lambert, likewise, endeavours
to supply this exigency by another means, — by the fortuitous quality
(his dottings) of certain lines. In our scheme lines, simple lines,
and lines alone, are sufficient.
5°, Consistent. — Lambert's linear scheme is a mere jumble of
inconsistencies. Compared with his, those by figures are, in this
respect, far jjreferable. But the present linear scheme is at once
thorougho-oins;, unambiguous, and consistent.
6°, Manifest. — In this essential condition, all other geometrical
illustrations are lamentably defective. In those by figure, each
threefold diagram, typifying an indefinite plurality of moods, re-
quires a painful consideration to extract out of it any pertinent
elucidation ; this is, in fact, only brought to bear by the foreign
aid of contingent symbols. Nor can these schemes properly re-
present to the eye the relation of the toto-total identity of a plu-
rality of terms ; the intention requires to be intimated by the ex-
ternal accident of signs. Lambert's lines sink, in general, even
below the figures, in this respect. But as lines are here applied,
the sole pertinent inference leaj)s at once to sense and under-
standing.
7°, Precise. — Ambiguity, vagueness, vacillation, redundancy, and
withal inadequacy, prevail in the other schemes. In those by
figure, one diagram is sometimes illustrative of as many as a dozen
moods, positive and negative ; and a single mood may fall to be
represented by four diagrams, and perhaps in six several ways.
Lambert's lines are even worse. In our scheme, on the contrary,
every mood has a diagram applicable to itself, and to itself exclu-
sively, whilst every possible variety of its import has a correspond-
ing possible variety of linear difference.
8°, Complete. — In this last and all-important condition, every
scheme, hitherto proposed, is found to fail. A thoroughgoing,
adequate, and pliant geometric method ought equally and at once
to represent the logical moods in the Unfigured and Figured Syllo-
gism, in the Syllogism Synthetic and Analytic, in Extension and
Intension, — this, too, in aU their mutual convertibilities, and in all
their individual varieties. This our scheme performs ; but exclu-
4G8 APPENDIX.
sively. So much, in general. Again, in particular : — Of the
figures, circles and triangles are necessarily inept to represent the
ultra-total inclusion or coexclusion of terms, — in a word, all the
relations of jjroportion, except totality and indefinite partiality ;
whilst quadrilateral figures are, if not wholly incompetent to this,
operose and clumsy. Lambert's linear method is incompetent to
it in negatives ; and such inability ought to have opened his eyes
upon the defects of his whole plan, for this was a problem which
he expressly proposed to accomi}lish. The present scheme, on the
other hand, simply and easily joerforms this, in affirmation and
negation, and with any minuteness of detail.
Author's Scheme of Notation — Unfigured and Figured
Syllogism — No. II.
(1853.) The following Diagram affords a condensed view of
my other scheme of Syllogistic Notation, fragments of which, in
detail, will be found in Mr Thomson's Outline of the Laws of
Thought, and in Mr Baynes' Essay on the New Analytic of
Logical Forms. The paragraphs appended will supply the neces-
sary explanations.
APPENDIX.
469
Breadth
»»»»»
Order
Ei ihcr or ]S!e i iJi er.
1.) A Proposition, (hiaarr]ixa,intervallum,'Trp6Tacn^, literally
X)rotensio, the stretching out of a line from point to point), is a
mutual relation of two terms {ppoC] or extremes (aKpa). This is
therefore well represented, — The two terms, by two letters, and
their Eelation, by a line extended between them.
2.) A Syllogism is a complexus of Three Terms in Three Pro-
positions.— It is, therefore, adequately typified by a Triangle,— by
a Figure of three lines or sides.
470 APPENDIX.
3.) As upwards and downwards is a procedure arbitrary in the
diagram, the diagram indicates that we can, indifferently, either
proceed from the Premises, (rationes), to the Conclusion {ratio-
natuni), or from the Conclusion to the Premises ; the process
being only in different points of view, either Synthetic or Ana-
lytic. (An exclusive and one-sided view, be it remembered, has
given an inadequate name to what are called Premises and Con-
clusion.)
4.) Eationally and historically, there is no ground for consti-
tuting that Premise into Major which is enounced first, or that
Premise into Minor which is enounced last. (See after, p. 697,
&c.) The moods of what is called the Fourth Figure, and the In-
direct moods of the First Figure, are thus identified. — In the
diagram, accordingly, it is shown, that as right or left in the order
of position is only accidental, so is first or last in the order of
expression.
5.) The diagram truly represents, by its various concentric
triangles, the Unfigured Syllogism, as involving the Figured, and,
of the latter, the First Figure as involving the two others. (In
fact, the whole differences of Figure and Figures are accidental ;
Moods alone are essential, and in any Figure and in none, these
are always the same and the same in number.)
6.) Depth and Breadth, Subject and Predicate, are denoted by
the thick and thin ends of the same prepositional line.
7.) Depth and Breadth are quantities always coexistent, always
correlative, each being always in the inverse ratio of the other. —
This is well shown in the connection and contrast of a line gradu-
ally diminishing or increasing in thickness from end to end.
8.) But though always coexistent, and consequently, always,
to some amount, potentially inferring each other, still we cannot,
without the intervention of an actual inference, at once jump
from the one quantity to the other, — change, per saltum, Predicate
into Subject and Subject into Predicate. We must proceed gra-
APPENDIX. 471
datim. We cannot arbitrarily commute the quantities, in passing
from the Qusesitum to the Premises, or in our transition from the
Premises to the Conclusion. When this is apparently done, (as in
the Indirect moods of the First Figure and in all the moods of the
Fourth), the jDrocedure is not only unnatural, but virtually complex
and mediate ; the mediacy being concealed by the concealment of
the mental inference tuhich really precedes. — Indicated by the
line and broken line for the First Figure.
9). In Syllogism, Figure and the varieties of Figure are deter-
mined by the counter relations of Subject and Predicate subsisting
between the syllogistic terms, — between the Middle and Extremes.
— All adequately represented.
10.) Figure and the differences of Figures aU depending upon
the difference of the mutual contrast of Subject and Predicate
between the syllogistic terms ; consequently, if this relation be
abolished, — if these terms be made all Subjects, (or it may be all
Predicates), the distinction of Figure will be abolished also. (We
do not abolish, be it noted, the Syllogism, but we recall it to one
simple form.) — And this is represented in the diagram. For as
the opposition of Subject and Predicate, of Depth and Breadth, is
shown in the opposition of the thick and thin ends of the same
tapering line ; so where, (as in the outmost triangle), the preposi-
tional lines are of uniform breadth, it is hereby shown, that all
such opposition is sublated.
11.) It is manifest, that, as we consider the Predicate or the
Subject, the Breadth or the Depth, as princii^al, will the one pre-
mise of the Syllogism or the other be Major or Minor ; the Major
Premise in the one quantity being Minor Premise in the other. —
Shown out in the diagram.
12.) But as the First Figure is that alone in which there is such
a difference of relation between the Syllogistic Terms, — between
the Middle and Extremes ; so in it alone is such a distinction between
the Syllogistic Propositions realised. — By the diagram this is made
apparent to the eye.
472 APPENDIX.
13.) In the Unfigured Syllogism, and in the Second and Third
Figures, there is no difference between the Major and Minor Terms,
and, consequently, no distinction, (more than one arbitrary and
accidental), of Major and Minor Propositions. — All conspicuously
typified.
14.) All Figured Syllogisms have a Double Conclusion ; but
in the different figures in a different way. — This is well repre-
sented.
15.) The Double Conclusions, both equally direct, in the Second
and Third Figures, are shown in the crossing of two counter and
corresponding lines. — The logicians are at fault in allowing Indi-
rect Conclusions in these two figures, — nor is Aristotle an excej)-
tion. (See Pr. An., I., vii. § -i.)
16.) The Direct and Indirect Conclusions in the First Figure
are distinctly typified by a common and by a broken line ; the
broken line is placed immediately under the other, and may thus
indicate, that it represents only a reflex of, — a consequence through
the other, (/car avaKkacriv, reflexim, ^;cr rejiexionem). The
diagram, therefore, can show, that the Indirect moods of the First
Fio;ure, as well as all the moods of the Fourth, ought to be re-
duced to merely mediate inferences ; — that is, to conclusions
from conclusions of the conjugations or premises of the First
Figure. «
[The following Table affords a view in detail of the Author's
Scheme of Syllogistic Notation, and of the valid Syllogistic Moods,
(in Figure), on his doctrine of a quantified Predicate. In each Figure,
(three only being allowed), there are 12 Affirmative and 24 Nega-
tive moods ; in all 36 moods. The Table exhibits in detail the 12
Affirmative Moods of each Figure, and the 24 Negative Moods of
the First Figure, with the appropriate notation.
* rieprinted fi-oiu Discussions, p. 6^7-061. — Ed.
APPENDIX. 473
The letters C, V, each the third letter in its respective alphabet,
denote the extremes ; the letter M denotes the middle term of the
syllogism. Definite quantity, (allj any), is indicated by the sign
(:) ; indefinite quantity, (some), by the sign (, or ,). The hori-
zontal tapering line ( » ) indicates an affirmative relation
between the subject and predicate of the proposition. Nega-
tion is marked by a perpendicular line crossing the horizontal
( ^ I )■ The negative syllogisms, in all the Figures, are exactly
double the number of the affirmative ; for every affirmative
affords a double negative, as each of its premises may be marked
by a negative. In Extension, the broad end of the line denotes
the subject, the pointed end the predicate. In Comprehension
this is reversed ; the pointed end indicating the subject, the
broad end the predicate. By the present scheme of notation,
we are thus able to read a syllogism both in Extension and in
Comprehension. The line beneath the three terms denotes the
relation of the extremes of the conclusion. Predesignation of
the conclusion is marked only when its terms obtain a different
quantity from what they hold in the premises. Accordingly,
Avhen not marked, the quantification of the premises is held re-
peated in the conclusion. In the Second and Third Figures, — a
line is inserted above as well as below the terms of the syllogism,
to express the double conclusion in those figures. The symbol
^-^y — ' shows that when the premises are converted, the syllogism
remains in the same mood ; ^^^><:^ shows that the two moods
between which it stands are convertible into each other by con-
version of their premises. The middle term is said to be Balanced,
when it is taken definitely in both premises. The extremes are
balanced, when both are taken definitely ; unbalanced, when the
one is definite, and the other is not.
The Table here given exhibits the author's final arrangement
of the Syllogistic Moods. The Moods are either A), Balanced, or
B), Unbalanced,. In the former class both Terms and Propositions
are Balanced, and it contains two moods, — i. ; ii. In the latter
class there are two subdivisions. For either a), the Terms are
Unbalanced, — iii. iv. ; or b), both the Terms and Propositions are
Unbalanced, — v. vi. ; vii. viii. ; ix. x. ; xi. xii.
It should be observed that the arrangement of the order of
Moods given in the present Table, differs from that of the earlier
474; APPENDIX.
scheme printed above, p. 287 et seq. The following is the corre-
spondence in the order of moods : —
Present and
Final Table.
Earlier
Table.
I.
corresponds to
I.
II.
... ...
II.
III.
... ...
XI.
IV.
XII.
V.
... ...
VII.
VI.
VIII
VII.
III.
VIII.
... ...
IV.
IX.
... ...
V.
X.
... ...
VI.
XI.
... ...
IX.
XII.
X.
The order of the earlier table is that given by Mr Baynes, in the
scheme of notation printed at p. 76 of his Essay on the New Ana-
lytic. The order of the present table corresponds with that given
by Dr Thomson in his Laivs of Thought, p. 244, 3d edition, 1853.
—Ed.]
APPENDIX.
4«.')-(j
SCHEME OF NOTATION— FIG U If ED SYLLOGISM.
TABLE OF SYLLOGISTIC MOODS.
Fig. I
M:
A. AFFIRMATIVE MOODS.
Fig. II.
Fig. III.
; : M: iF C: : M : :r C:- •• M : -T . f
I. i
B. NEGATIVE MOODS.
Fig. I.
a C:-+— ■ M : :r
C, : M : — ..r C, : M : — ,r C- : M : ^.r
C-
: M,
■•r C'-
M,
:r C
M
1 b c=
a C. 4—
b C.
j a C> ^
b C-
M
M
M
. M
-.r C:
,M: ,r C>
, M
-.r
/ V. C. : M, ^.r C,^ : M , ^,r c.- — ■- M , — ,r
B
j a C: H— . M •■ ^ .r
{ b C: ^ ' M : -|- ,r
a C. 4— = M , ,r
:M,
b C'
j a C
,M
C. , M : .,r C, , M : — ,r C, , M : ,T ''■ | ^ C, , M
vii. C
viii. C-
ix. C:-
»-
X. C:-
xi. C:-
: :M: ..r C: :M: ,r C-" - ^ '■ 'T vii. \
a C:
: M
M,
, M:
:M,
.:r
c,
:r
C:-
>'
:r
C:-
,r
C:-
: M
:M,
,M:
M,
:r
c
.r
c
T
c
r
c'
: M
:M,
, M:
:U,
-:r
■T
[ b C:
a G, -\—
b C. ■
( a C:-f— _
( b C=
a C:H--_
b C=
I a C:-]—
M
M
,r
.r
,r
,r
,r
:r
:r
.r
M. j--:r
-.T
M
M
M,
.¥
t:
{ b C: ■ :M,
C, , M : :r C, , M : 'r C» » M : ..r
a C,-t— . M :
b C, M :
,r
,r
■.r
•r
A. i. and ii. are Balanrrrl. B. The other moods are Unbalanced. Of these, iii. and iv. are unbalanced in terms only, not in propo.sitions ; the rest in both.
INDEX.
AbstrajCT or General Logic, see Logic.
Abstraction or Generalisation, what, L
123 ; 1-17-8 ; its synonyms, ib.
Academical Disputation, ii. 224r-5.
Accidents, or Extrinsic Denominations,
what, i. 217.
Acquisition of Knowledge, doctrine of,
see Logic.
Affections or Passions, as a source of
error, see Error, Causes of.
Afranius, quoted on the nature of exi)e-
rience, ii. 1.56.
Agi-icola, Rodolphus, i. 2S2.
Albertus ^Magnus, referred to on genus
of Logic, i. 9 ; quoted on province of
Logic, 27 ; quoted on quantification of
predicate, ii. 309-10.
Aldrich, Dean, his Comjiendiiim, i. 29 ;
his abusive employment of the terms
hypothetical and conditional, 236 ; his
abuse of the phrase in-opositio erposiia,
263 : 350.
Alexander of Aphrodisias, the oldest com-
mentator on Aristotle, i. 5 ; referred
to as to his use of the term \oyiK^,
ib. ; has the distinction of Abstract
or General and Applied or Special
Logic, 53 ; his illustration of the dis-
tinction, 53-4, see Logic ; 2S2 ; 2S3 ;
on principle of name of major and
minor terms, 294 ; 306 ; 33S ; referred to
on quantity of hypothetical syllogisms,
348 : 391 ;" 414 ; ' ii. 3 ; -256 ; quoted on
quantification of predicate, 303 ; his
ground of the discrimination of major
and minor terms in the second and third
Figures, 40S-9 ; certain early Greek
logicians mentioned by, who recognised
no major or minor term in the second
and third Figm-es, 409-10 ; (and Her
minus), quoted on figure of syllogism,
415-20.
Alexander de Ales, or Alensis, held the
law of Contradiction to be the primaiy
principle of knowledge, i. 92 ; but, in
fact, identified it with that of Ex-
cluded Middle, ib.
Alstedius, on the principle of Contradic-
tion, i. 88 : partially anticipated Lana-
bert in the use of parallel lines as logi-
cal notation, 256.
Alvarez, i. 456.
Ammonius Hermije, referred to on genus
of Logic, i. 9 ; 54 ; on the principle of
Contradiction, 88 ; 191 : 226 ; 245 ;
279 ; 33S ; 391 ; referred to on the
\6yos Bipi^wv, or reajier, 463 ; 466 ; ii. 3 ;
referred to on Division and its various
kinds, 22 ; referred to on Greek article,
280 ; quoted on q\iantification of pre-
dicate, 299, 303-6; quot«d on Hypo-
thetical (Conjunctive) and Disjunctive
Syllogisms, 388-92 ; (and Philoponus),
their ground of the discrimination of
major and minor terms in the second
and third Figures, 403.
Analogy, what, ii. 165-6 ; 170-71 ; founded
on the principle of Philosophical Pre-
sumption, 166 ; its agreement vith and
distinction from Induction. 166-7 ; has
two essential conditions, 171-2 ; sum-
mary of the doctrine of, 172 : Induction
and "Analogy compared together, 172-3 ;
these do no"t afford absolute certainty,
173-4 ; authors referred to on, 174.
Analysis, see Method.
Analytic, name employed by Aristotle to
denote a particular part of Logic, i. 8.
Anaximenes, of Lampsacus, the treatise
PJietoi-ic to Ale.rander attributed to, i.
390.
AnciUon, Frederic, referred to, i. 44.
Andreas, Antouius, the first to explicate
the law of Identity as a co-ordinate
principle, i. 91.
Anscftauunp, expresses what is common to
Perception and Imagination, as opposed
to Conception, viz.", the indiriduali^
andimmediacv of their objects, i. 126-7 ;
183 : can be" translated into English
only by Infu ition, but ambiguously, 127.
Ani/toloffia Grceca, i. 393.
'AirapiBfiricris, its character and meaning,
ii. 23.
Apodeictic, employed by Aristotle to de-
note a particular part of Logic, i. 8.
478
INDEX.
Apophantic^ nee Jvidg^ments, Doctrine of.
' h-K6(pav(ns, its use by Aristotle, i. 22(j.
Applied Loijic, the expression, Low em-
ployed by Kant, i. tiO ; can only with
propriety be used to denote Special or
Concrete Logic, and is improperly em-
ployed as a designation of Modified Lo-
gic, (il.
Apuleius, i. 414.
Aquinas, St Thomas, i. f<S ; referred to
on classification of the Categories, 200 ;
his definition of truth quoted, ii. G3.
Arabian Schoolmen, viewed Logic as a
science, i. 9.
'Apx^ TTjs Yi/wtrews, distinguished by Aris-
totle from the apxv'''V^ yeveaewSj i. 93.
Argument, properly denotes the middle
notion in a reasoning, i. 278 ; how de-
fined by the Latin Rhetoricians, 278-9 ;
often employed as coextensive with
argumentation, 279.
Aristotelic questions, An sit, &c., referred
to, ii. 158.
Aristotelians, ancient Greek, denied Logic
to be either science or art, i. 9 ; their
views on the object-matter of Logic,
27.
Ai-istotelians, modern, many of them main-
tained Logic to be an art, i. 9.
Ai'istotle, quoted, i. 5 ; his employment
of the term Dialect ie, 8 ; did not "define
liOgic, 9 ; his relation to views of the
nature and domain of Logic, 26-7 ; by
far the greater number of his logical
writings lost, 26 ; none of his treatises
affords a view of Logic from a central
point, ih. ; gave no general definition of
Logic, ih. ; said that medicine begins
where the philosoph}' of nature leaves
off, 36 ; emphatically enounced the law
of Contradiction, 87 ; explicitly enoun-
ced the principle of Excluded Middle,
90-1 ; recognised the law of Reason
and Consequent, 93 ; distinguished it
from the principle of Production, ih. ;
said that the doctrine of Syllogisms
deals not with the external expression,
but with the internal reasoniiig of the
mind itself, 115; see also 388; used
voy)fiara in a sense equivalent to con-
cepts, 120 ; his first anti-prEedicamental
rule quoted, 144 ; this rule translated
by the Nota notce e.<<t nota rei ipsius, ih. ;
his Categories, what, 196, see Categories;
n(jticed the difference of Potential and
Actual Wholes, 207 ; referred to on in-
clusion of Copula in prajdicate, 228 ;
called subject and predicate, the terms
or extremes of a proposition, ih. ; called
a proposition an Interval, Sidarrifia,
229 ; allowed only four kinds of modal-
ity, 257 ; described Sub-contrary oppo-
sition as merely in language, 261, see also
ii. 281 ; his conversion eV fj-epet, 264 ;
noticed Couversion^jfic Coiitrapositionem,
under the name of the inverse consecution
from contradictions, ih. ; his employment
of the tei-m (KOecrts, e.vposition, 263 ; his
expression for Simple Conversion, ih. ;
his A nali/lics are SjTithetic, 277 ;
see alio ii. 401 ; his definition of the
terms of a Syllogism, i. 299 ; his defini-
tion of the middle, as middle by posi-
tion, not applicable to the mode in
which subsequent logicians enounce the
syllogism, ih. ; but"" applicable to the
reasoning in comprehension, 299-300 ;
did not, however, necessarily contem-
plate the reasoning in comprehension,
300 ; enounced the canons both of Ex-
tensive and Comprehensive reasoning,
303 ; 342 ; his law,— that the whole is
necessarily conceived as prior to the
part, —criticised by the Author, 357-9;
only once vaguely alluded to the
process of what was afterwards called
Sorites, 375 ; his rule translated Pra;-
dicat/im pra-dicati, &c., contains the
principle of Sorites, ih. ; did not dis-
criminate the vulgar Enthymeme as
a distinct species of reasoning, 388-
9 ; his Enthymeme a syllogism from
signs and likelihoods, 389 ; Rhetoric
to Ale.rander attributed to, 390 ; the
term (Tx^)ixa, Figure, due to, 400; distin-
guished the first three figures, ih. ; 413;
415 ; 454 ; 466; ii., 6 ; his distinction of
the two modes of scientific procedure
as from, and to, principles, 8; 12; his
argument for slavery a petitio prin-
cipii, 53 ; referred to and quoted on
knowledge and belief, 70-1 ; his pre-
cept regarding the subjugation of self-
love, 102 ; 137 ; 206 ; quoted on ability
to teach as a mark of knowledge,
210; first systematically developed Logic
proper, 231 ; referred "to on postulates
of Logic, 552-3; quoted against quantifi-
cation of predicate, 298-303 ; the true
meaning of his e.fse in toto, and did
de omni, 301-2 ; his doctrine of prede-
signation, 302-3 ; syllogisms in his writ-
ings which are valiil only thi-ough quan-
tification of the pi-edicate, 302 ; 346 •
his doctrine of Induction and Example,
358-62 ; ignored the Disjunctive and
Hypothetical syllogisms of the logicians,
376 ; quoted and referred to on Hypo-
thetical syllogism, 387-8 ; his syllogisms
ex It >/pot/iesi, —whether correspon<lent to
the ordinary hypothetical syllogism, —
authors referred to on, 388 ; his doctrine
of the discrimination of major and minor
terms in the second and third Figure,
407 ; ipioted on Figure and Terms of syl-
logisms, 413-14.
Arnauld, along with Nicole, author or
the Port-Ro3'al Logic (L'Art de Penser),
i. 70 ; referred to as holding that men
are naturally envious, ii. 105 ; quoted
on figure of Syllogism, 426-7.
Arnoldus de Tungeri, his doctrine of In-
duction, ii. 367.
Arrian, referred to on the argmnent called
x6yos KvptevcDV, i. 464.
I
I
INDEX.
479
Arseniiis, i. 4GS.
Ai-t,' ancient and modern, diverse charac-
ters of, ii. 131-2.
Association, laws of, what, ii. r22-3.
Association or Suggestion, as a source of
Error, see Error, causes of.
Assumption, name for Minor Premise, i.
2S5 ; but not a suitable term, ib.
Attention, the act of, how constituted, i.
123 ; Prescision, Abstraction, and At-
tention correlative terms, 123.
Augustin, St, his answer to the question
what time is, i. 167.
Augustin, Pseudo, referred to on inapplica-
bility of the categories to Deity, i. 198.
Augustinvis Niphus Suessanus, i. 88.
Aulus Gellius, i. 464 ; 466.
Authenticitj', criticism of, see Testimony.
Averroes, quoted on use of the Ai'abic
article in quantification, ii. 2S0 ; quoted
on quantification of predicate, 309 ;
quoted on figure of syllogism, 425-6 ;
quoted on fourth Figure, 454.
Avicenna, ii. 167 ; 171.
Axioma, used by Stoics and Ramists as a
synonym iov jiropoyition, i. 266.
A^ioofia rris a,yTL(pd(recjt>s,^^Tiarao applied by
Ammonius and I'hiloponus to principle
of Contradiction, i. 88, see Contradic-
tion, principle of.
Axioms, what, i. 266.
Bachmann, referred to on the analogy
between Logic and Mathematics, i. 44 ;
94-5 ; 124 ; 210 ; 230 ; 254 ; 259 ; 282 ;
306 ; 309 ; 311 ; 334 ; 342 ; 404 ; quoted,
with brief or-iginal interpolations, on
the fig-ures and moods of Sjdlogism,
405-22 ; his reduction of Baroco, 440 ;
quoted on character of ancient Greek
Sophisms, 452-4 ; ii. 81 ; quoted on the
prejudice of learned authority, 87-8 ;
114-18 ; 134 ; 151 ; 174.
Bacon, Lord, wholly misconceived the
character of Logic in cei tain respects,
i. 29 ; at fault in his criticism of Aris-
totle's doctrine of Induction, 325; called
empirical generalisations axioms, ii. 47;
his classification of the sources of error,
80 ; quoted on reading, 223 ; the aim of
his Organon, 231.
Balfour, or Balforeus, referred to on a
spurious pas.sage in A.v\&iot\e's Rhetoric,
i. 8 ; quoted on illustration by the
Aphrodisian of Abstract and Applied or
Special Logic, 54 ; on Abstract and Ap-
plied or Special Logic, 62.
Ba0os, its meaning in relation to concepts,
i. 141.
Baumgarten, A. G., the Leibnitian, the
first to iise the term 2)>'i'ici2>i>i'it- exdusi
medii, i. 91 ; called the principle of
Identity, jmncipium positionis sive
■identitatis, 92 ; attempted to demon-
strate the law of SufBcient Eeason by
that of Contradiction, 95 ; 1 42 ; quoted
on Canons of Syllogism, ii. 324-5.
Baynes, Thomas Spencer, his Exsai/ on the
Neio A nalylie of Logical Forms referred
to, i. 42 ; his translation of the Port
Royal Logic noticed, 70; 162 ; his Essay
referred to, ii. 315.
Begriff, the tenn in German philosophy
for the symbolical notions of the under-
standing, i. 1 83.
Belief, see Truth and Error, doctrine of.
Ben Gerson, or Gersonides, Levi, quoted
on quantification of predicate, ii. .310-1 1.
Beneke, i. 95 ; his doctrine of syllogism,
ii. 439-42.
Bertius, i. 279 ; 375.
Beza, i. 3.93.
Biel, Gabriel, his use of conceptus, i. 42.
Biunde, ii. 63.
Blemmidas, Nicephorus, i. 119 ; referred
to on origin of distinction of proposi-
tions secundi and tertii adjacentis, 228 ;
quoted on import of the term ffvWo-
■yifffjiSs, 279, 384 ; his Epitome for many
contiu'ies the text-book of Logic in the
schools of the Greek Church, 432 ;
mentioned as the inventor of the Greek
mnemonic verses for mood and figure
of syllogism, 432; but, according to
later view, these verses only a transla-
tion of the Latin, 432: ii. 256; quoted
on Contingent Conversion, 265.
Boethius, referred to on the application of
the term logic, i. 5, 142, 156 ; his divi-
sion of Conversion, 264 ; the first to
give the name C'oiiversio per accidens,
ib. ; nature of this process as employed
by, ih., 282; quoted for wse oi sumptum
OAvl asmmplio, 285; referred to on use
of terms poucus and tollens, in connec-
tion with hypothetical syllogism, 338,
414 ; ii. 14 ; quoted on the influence of
passion on the mind, 94 ; 256 ; quoted
on quantification of predicate, 306-9.
Bolzano, i. 33S ; 344; ii. 174.
Bojde, Hon. Robert, referred to for dis-
tinction of reason iJi ahstracto, and rea-
son in coiicreto, i. 60.
Brandis, Ch. A., referred to on the title
Organoti for the logical treatises of
Aristotle, i. 34 ; 191.
Braniss, Ch. J., i. 262 ; 448.
Breadth and Depth, names for the exten-
sion and comprehension of concepts, i.
141 et alibi.
Buchanan, George, i. 393.
Buffier, i. 159 ; ii. 14 ; quoted on canons
of syllogism, 337-8.
Burgersdyk, or Burgersdicius, referred to
on genus of Logic, i. 9 ; his Institvtioiies
Logicce noticed and recommended, 71 ;
ii. 225 ; referred to on Whole and Part,
202 ; quoted on Potential and Actual
Whole, 206-7 ; 415.
Buridanus, his sophism of the Ass re-
ferred to the head of Sophisma Hetero-
zeteseos, i. 466.
Burleigh, Lord, his practice in reading,
ii. 216-17.
480
INDEX.
Butler, Samuel, quoted as to tte princi-
pal utility of Rhetoric, i. 48.
Cajetan, Cardinal, quoted for his use of
the terms intensive and extensive in rela-
tion to notions, i. 141.
Calker, i. 141.
Camerarius, Gul., referred to on g'enus of
Logic, i. 9 ; referred to for scholastic
theories on the object-matter of Logic,
27-8.
Campbell, Principal, quoted on indis-
tinctness of terms, i. 175-6.
Capella, Martianus, quoted on figure of
syllogism, ii. 424-5.
Caramuel, see Lobkowitz.
Carleton, Thomas Compton, referred to
on tho metaphysical character of the
Categories of Aristotle, i. 199.
Caro, quoted, ii. 104-(j ; 114 ; 144.
Cartesians, majority of, maintained Logic
to be an art, i. 9.
Cassiodorus, i. 392 ; ii. 424.
Categorical Proposition, better styled
Absolute or Perfect, i. 233, see Judg-
ments, doctrine of.
Categorical, the term, as used by Aris-
totle, equivalent to affirmative, i. 234 ;
its application by Theophrastus and
Eudemus, in opposition to conclitiottal,
234-5 ; this difference of signification
not hitherto observed, 235.
Categories or Predicaments of Aristotle,
what, i. 19(3 ; original meaning of the
term Category, 197 ; its employment by
Aristotle, ih. ; by Plotinus, ih. ; by
Kant, 197-8 ; the Categories of Aris-
totle metaphysical, 199 ; criticised as a
classification of being, 199-200; objects
not included under, 198 ; diversity of
opinion among logicians regarding
their number, 200 ; various authors
referred to i-egarding, 200-1.
Certainty, see Truth and Error, Doctiine of.
Chauvin, i. 265.
Cicero, referred to on the use of Logica,
i. 6 ; probably borrowed his use of that
term from the Stoics, ih. ; quoted on
the province of Logic, 37 ; enounced
the principle of Excluded Middle, 91 ;
recognised the principle of Reason and
Con.sequent, 93 ; his definition of argu-
mentum quoted, 279 ; applied the term
Sorites to an argument like the modern
Sorites, but which coxdd also be a
Chrifsippean, 376 ; called the sophism
Sorites Acervalis, ib. ; his employment
of the term Hitthi/meme, 390 ; his state-
ment of the /yHara liatio, 462; 465-6;
ii. 103; 206-7.
Circulus in demonstrando, see Probation.
Classes, names for the different steps in
the series of, in physical science, i. 201.
Clearness and Obscurity, Distinctness and
Indistinctness of Concepts, see Con-
cepts, Quality of.
Clement of Alexandria, quoted on teach-
ing as a mean of self-improvement in
knowledge, ii. 210.
Clerc, see Le Clerc.
Cogitatio (Thovght), its use by Descartes,
i. 12 ; see Thought.
Cognitive Faculties, Weakness and Dis-
proportioned Strength of, as a source
of error, see Error, Causes of.
Coke, Zachary, his use of the term con-
cept, i. 42.
College of Alcala, the, see Cursus Complu-
tensis.
Communication of Knowledge, Doctrino
of, see Logic.
Comparison, Faculty of, its products
threefold, — Concepts, Judgments, and
Reasonings, i. 117 ; its offices, 122-3.
Comprehension and Extension of Con-
cepts, see Concepts, Quantity of, cuid
Reasonings.
Concept, should be used to denote the ob-
ject conceived, i. 41-2 ; its derivation,
42 ; many words in English formed on
the same analogy as precept, digest, &.C.
ib. ; was in common use in the sense
proposed among the older English
philosophical writers, ib. ; and among
the old Fi-ench philosophers, ib. ; now
employed in French in translating the
German Begriff, ib., see also Conceptus;
what, 76 ; its synonyms, 76-7 ; see Con-
cepts, Doctrine of.
Conceptio, its meaning, i. 120.
Conception, employment of the term by
Stewart to denote the simple represen-
tation of an object presented in Percep-
tion, i. 40 ; vacillation in its use by
Reid, ib. ; sense in which employed by
the author, ib. ; its derivation, 41 ;
means both the act of conceiving and
the object conceived, ib. ; should be
used to denote exclusively the act of
conceiving, and concept applied to the
object conceived, 41-2 ; Reid quoted
on, 109-12 ; his mistakes regarding,
112-13 ; usually called by the logicians
Simple Apprehension, 119.
Concepts, Doctrine of, i. 116-24 ; of Con-
cepts or Notions, order of discussion, —
A. In general, what they are, and how
produced, 118 et seq., 130 et seo. ; doc-
trine of concepts omitted by Whately
in his Elements, 118 ; a. Meaning of the
terms Concept or Notion, 119-20 ; their
synonyms, 119 ; Concept denotes the re-
sult of the act of Conception, that is,
of comprehending or grasping up into
unity the various qualities by which an
object is characterised, 120 ; Notion
denotes either the act of apprehending
the notes or marks of an object, or the
result of that act, ib. ; employment of
the terms animo vel mente concipere, and
aninii conceptus, ib. ; of concipere, con-
ceptus and concej)tio, without adjunct, ib. ;
the term Notion how employed by the
author, 121 ; b. Nature of the thing ex-
INDEX.
481
pressed, 121 et seq.; a concept eqiiivalent
to the mediate and relative knowledge we
have of an object, as comprising qualities
or characters common to it with other
objects, 122 ; nature and production of
concepts illustrated by reference to the
history of our knowledge, 122 et seq. ;
the results of comparison and abstrac-
tion or attention, as operating on ob-
jects originally presented in confused
and imf)erfect perceptions, and reducing
multitude to unity, 122-4 ; the reduc-
tion of multitude to unity involved in
conception explained and illustrated,
124 et seq. ; thought one and the same,
while its contents are identical, 124 ;
objects are to us the same when we are
unable to distinguish their cognitions,
whether as wholes, or in their partial
characters, 124-5; concepts or notions
are constituted by the points of similar-
ity discovered in objects, and identified
in the unity of consciousness, 125 ;
concepts may themselves become the
objects of comparison and abstraction,
12b" ; concepts or notions superfluously
styled, (leaeral, ih.; general characters of
concepts, 127 el seq., Vii: et seq. ; a. A
concept affords only an inadequate
knowledge of the thing thought under
it, 127 et seq. ; b. Affords no absolute
object of knowledge, but can be realised
only by being applied as a term of rela-
tion to one or more of the objects
which agree in the point or points of
resemblance which it expresses, 128 ;
this doctrine explains the whole mystery
of generalisation and general terms, ib. ;
the generality of a concept is potential,
not actual, 129-35 ; concepts are not,
on that account, mere words, 136 ; c.
Their dependence on language, 137 et
seq. ; language necessary to the perfec-
tion of concepts, 139 ; B. Of concepts
or notions in special, 140 et seq. ; quantity
of concepts, 141 et seq.; what is meant
by saying that a concept is a quantity,
143 ; this quantity of two opposite kinds,
— Intensive or Comprehensive and Ex-
tensive, 143-5(1, see Concepts, Quantity
of; quality of Concepts, 157-86, ^eg Con-
cepts, Quality of ; Reciprocal Relations
of, 187 et seq., see Concepts, Reciprocal
Relations of.
Concepts, Quantity of, or Comprehension
and Extension of Concepts, what, i.
141-3, 146 ; how respectively desig-
nated, 141; these quantities opposed
to each other, 146 ; law regulating
the mutual relations of, il>. ; this il-
lustrated, 147 ; processes by which
amplified and resolved, — Determination
or Concretion, Abstraction or General-
isation, Definition, and Division, 143-7;
opposed in an inverse ratio, 14S-9 ; De-
finition and Division the processes by
which the Comprehension and Extension
of concepts are respectively resolved.
149-51 ; diagram representing, with re-
lative illustration, 152-6.
Concepts, Quality of, i. 157 et seq. ; this
determined by their relation to their
subject, 157 ; consists in their logical
perfection or imperfection, 157, 158 ;
this of two degrees, — Clearness and
Distinctness, and Obscurity and In-
distinctness, 158 ; these degrees distin-
guished, 158-9; original application of
the expressions clearness, obscurity, &c.,
159 ; illustrated by reference to vision
and representation, 159-60 ; 163-5 ;
clearness and obscurity as in concepts,
160 et seq.; the absolutely clear and the
absolutely obscure, 161 ; distinctness
and indistinctness of, l62 ; historical
notices of this distinction, 162 et seq. ;
due to Leibnitz, 162 ; notice of Locke
in connection with it, ib. ; difference
between a clear and distinct knowledge
illustrated, 163 et seq. ; the judicial de-
termination of life and death sujiposes
the difference between a clear and dis-
tinct knowledge, 164 ; further illustra-
tion from the human countenance, 164-
5 ; special conditions of the distinctness
of a concept, and of its degrees, 165-7 ;
the distinction between clear and dis-
tinct knowledge illustrated by examples,
167 ; how the distinctness of a concept
is affected by the two quantities of a
concept, 168 et seq. ; distinctness is in-
ternal and external, 168-9 ; relations of
Definition and Division to internal and
external distinctness, 169 ; simple no-
tions admit of an extensive, individual
notions of an intensive, distinctness,
169 ; the highest point of the distinct-
ness of a concept, 169-70 ; imperfection
to which concepts are liable, in respect
of the thought of which they are the
expression, 171-2 ; this imperfection
illustrated, 172 et seq. ; noticed by
British philosophers, 174 ; Stewart
quoted on the subject, 17^-7 ; Locke
anticipated Hume in remarking the
employment of terms without distinct
meaning, 177 ; Locke quoted on this
point, 177-9 ; the distinction of Intuitive
and Symbolical knowledge first taken
by Leibnitz, 179 ; this distinction su-
perseded the controversy of Nominalism
and Conceptualism in German}', 179-83 ;
discussed by him in De Cognitione, Veri-
late, et Ideis, 180 ; the passage quoted,
181-2 ; the distinction appreciated by
the disciples of Leibnitz, 183 ; Wolf
quoted on, 184-6.
Concepts, Reciprocal Relations of, i. 187-
224 ; relation proper of, what, 187 ; can
be compared together with reference
only either, 1°, To their Extension, or, 2°,
To their Comprehension, i6. ; considered
A. As dependent on extension, 187-212 ;
as dependent on extension, concepts
stand to each other in the five mutual
relations of Exclusion, Coextension,
482
INDEX.
Subordination, Co-ordination, and In-
tersection, 1S7-S ; examples of the five
mutual relations of concepts, 188 ; dia-
grams illustrative of, 189 ; of these
relations, sub-ordination and co-ordina-
tion of principal importance, ISO ; sub-
ordination considered, 190-209; terms
expressive of the different modes of the
relation of stibordination, 190 ei seq. ;
Superior, Inferior, Broader, Narrower
Notions, 190; Universal, Particular,
190-1; General Notion, Genus, Special
Notion, Species, 191-2, «'(?e Genus and Spe-
cies ; Co-ordination, what, 209; the two
general laws by which subordination and
co-ordination umk'r extension are regu-
lated, viz., of Homogeneity and Hetero-
geneity, 209-10 ; their import, 210 ; law
of Heterogeneity, true only in theory,
ih. ; additional law of Logical Affinity
promulgated by Kant, but to be rejected,
211 ; B. As dependent on compre-
hension, but not in the relations of
involution and co-ordination, 212-24 ;
notions, in relation to each other, are
Identical and Different, 212 ; identical,
divided into absolutely and relatively
identical, 212 ; alisolutely identical
notions impossible, 212-13; relatively
identical called also Similar and Re-
ciprocating or Convertible, ih. ; notions
are Congruent or Agreeing, and Con-
flictive, 213-14 ; Congruent and Identi-
cal notions, and Diverse and Conflictive
distinguished, 214, see Concepts, Oppo-
sition of ; Intrinsic and Extrinsic, 21 (i-
17 ; Involution and Co-ordination in
comprehension, 217, 220 ; these rela-
tions of notions neglected by logicians,
and hence also neglected reasoning in
comprehension, 217 el seq. ; the rela-
tion of the containing and the contained
in comprehension properly called in-
volution, 220 ; this illustrated, 220-21 ;
the involving notion the more complex,
the involved the more simple, 222 ; co-
ordination in comprehension, 223-24 ;
notions coordinated in comprehension
called Disparate, in extension Disjunct
or Discrete, 224.
Concej^ts, Opposition of, arises un der Com-
prehension, i. 213; constituted by con-
tiiction, or the imiiossibility of being
connected in thought, ih. ; twofold, 1*^,
Immediate or Contradictory ; 2°, Medi-
ate or Contrai-y, 213-14; these distin-
guished and illustrated, 214-15 ; their
logical significance, 215-l(i, set Opposi-
tion, of Propositions.
Conceptualism and Nominalism, the
whole controversy originated in the
ambiguity of words, i. 128, 136; how to
be reconciled, 128; this question not
agitated in Germany, ih.
Coua'jitus, its use by Biel, Occam, i. 42 ;
Coiueptus, and conceptus animi, its
meaning, 120.
Concipcre, its meaning, i. 120.
Conclusion, of a syllogism, what, i. 281 ;
its synonyms, ih. ; is the problem stated
as a decision, 282.
Concrete or Special Logic, see Logic.
Condillac quoted on influence of Associa-
tion, ii. 126-7 ; 171.
Conditional Judgment or Proposition, see
Judgments, Doctrine of.
Conditional and lli/pothetieal, variations
in regard to the application of the
terms, i. 236 ; Boethius, used conditiou-
alis (conditional) and hypothetinis (Itypo-
t/ietiaU) as convertible, ih. ; conditional
to be applied to the genus as including
hj/pothetical and <lisjiuictife, 237.
Conference, see Knowledge, Doctrine of
the Acquisition and Perfecting of.
Confucius, his remedy for precipitation,
ii. 98. _
Conimbricenses, i. 262 ; their error re-
garding the op)position of Boethius and
Averroes to Aristotle on quantification
of predicate, ii. 308.
Conspecies, what, i. 209 ; in so far as they
are considered diflerent, but not con-
tradictory, called Discrete or Disjunct
Notions, (7;.
Contingent Conversion, of the Lower
Greeks, what, ii. 264-5 ; Blemmidas
cited on, 265.
Contradiction, or Non - Contradiction,
princij)le of, a fundamental law of
thought, i. 79 ; what, 81 ; properly the
law of Non-Contradiction, 82 ; how
enounced, ib. ; the principle of all
logical negation and distinction, ib. ;
differs from the law of Identity only by
a negative expression, 83 ; its history,
87 et seq. ; can be traced back to Plato,
87 ; emphatically enounced by Aristotle,
87-8 ; with the Peripatetics and School-
men the highest principle of knowledge,
88 ; obtained its name from the Greek
Aristotelians, ih. ; said by Anmionius
and Philoponus to be the criterion
which divides truth from falsehood
throughout the universe of existence,
ib. ; said by Suarez to hold the same
supremacy among the principles of
knowledge which the Deity does among
the principles of existence, ib. ; contro-
versies touching its truth and axiomatic
character, 88-9; its truth denied by
modern absolutists, 89 ; how viewed by
Schelling and Hegel, 90 ; along with
that of Identity, regulates the categori-
cal syllogism, 249, 353 ; authors referred
to on, ii. 246 ; conditions of, ih. ; proof
of, attempted by Ciauberg, ih. ; see
Fundamental Laws of Thought.
Contus, Sebastianus, ii. 308.
Conversion /)er accidens, what, i. 264 ;
Conversion eV p-^pei, not the mere syn-
onym of, ii. 271 ; differently defined by
different logicians, 272 ; by Boethius,
ib. ; by logicians in general, ih. ; as am-
pliative, not logical, 264 ; as restric-
ti\'e, fortuitous, or not a conversion, ib.
INDEX.
483
Conversion, of Jud;j:ments or Propositions,
i. 2(52-7 ; what, 262 ; see also ii. 250 ; terms
employed to denote tlie orifrinal and
converted proposition, ib. ; the original
proposition ought to be called the C'o/i-
vertend or C'onverlihle, the product of
the conversion, the Converted or Coii-
vei'se, 261, 262 ; see also ii. 256, 266 ;
species of conversion distinguished by
logicians, 263-4 ; 1, Simple or Pui-e,
263-4 ; 2, Conversio per Accidens, 264 ;
this name first given by Boethius, ib. ;
3, Conversio per Contrapositionem, lb. ;
divisions of, by Boethius, ib. ; mne-
monic verses for conversion, 264-5 ;
definitions of, in general, ii. 256 ; a case
of immediate inference, ib. ; names
for the proposition given in, and its
product, 256-7 ; best names for these
together, C'onverteiit or Coiivei-ting, and
for each apart, Converfeiid and Con-
verse, ib., 266 ; errors of the common
logical doctrine of, two — first, That the
quantities are not converted with the
quantified terms, 257-S, 276 ; this wrong
shown, 1°, Because the terms of a pro-
position are only terms of relation, 257 ;
2°, Only compared as quantities, i6. ; 3",
Quantity of proposition in conversion
remains alwaj's the same, 257-S, 271 ;
4'^, Of no consequence logically whether
subject or predicate placed first, 258 ;
second error — The not considering that
the predicate has always a quantity in
thought as well as the subject, 258-63 ;
see also 271-4, 276 ; only one species
of, and that thorough-going and self-
sufficient, 264 ; conversio /^er accidens,
as arapliative, not logical, and as re-
strictive, merely fortuitous, ib. ; see also
271-2, see Conversion ;;er accidens ; Con-
versio ji&r contrapositionem, only holds
through contradiction, and is indepen-
dent of conversion, ib. , see Conversion per
contrapositionem ; the Contingent Con-
version of the lower Greeks, not a con-
version, 265, see Contingent Conversion ;
advantages of the author's own method
over those of the logicians, 2i55-6 ; the
character of, as given by Gi-eek lo-
gicians subsequent to Aristotle correct,
266 ; errors of Aristotle and the logi-
cians regarding, 266, 274-6 ; authorities
referred to on, 274-5.
Conversion per contra,positionem, only
holds through contradiction, and is not
properly a conversion, ii. 264-5, 275 ;
held by some to he mediate, 264 ; this
erroneous, ib. ; rules for, ib. ; historical
notices of, and authors referred to on,
264-5.
Conversion ^v fiepa, its meaning in Aris-
totle, ii. 271-2.
Co-ordination of concepts, see Concepts,
Relations of.
Copula, the logical, what, i. 228-9 ; in-
cluded in the predicate by Aristotle,
^b. ; styled the Appredicate, irpodKary]-
VOL. II.
yopovjxevov, ib. ; that negation does not
belong to, held by some logicians, 252 ;
the opposite doctrine maintained by
the author, ib. ; true import of, 252-3 ;
origin of the controversy regarding the
place of negation, 253 ; its meaning in
Comprehensive and Extensive proposi-
tions, 274.
Coraxand Tisias, caseof, referred to, i. 468.
Corollaries, what, i. 266.
Corvinus, quoted on inference from pure
particulars, ii. 457.
Cousin, Victor, his contradictions on the
cognition of the Absolute, i. 90.
Crakanthorpe, i. 230 ; referred to on
names of propositions in conversion,
263, 324 ; 367 ; his doctrine of Induc-
tion, ii. 367.
Crellius, i. 54 ; 325 ; 342.
Crenius, ii. 97 ; 210.
Criticism, Art of, see Testimony.
Crousaz, ii. 93 ; quoted in illustration of
precipitancy, ii. 97-8 ; quoted on sloth
as a source of error, 99 ; 137 ; 141.
Crusius, Christian August, ii. 109; quoted
on canons of sj'llogism, 320-22.
Cursiis Complutensis, referred to on in-
duction of Aristotle, ii. 364.
Custom, power of, as a source of error,
see Error, Causes of.
D'Abra DE Racoxis, referred to for scho-
lastic theories of the object-matter of
Logic, i. 28.
Damascenus, Joannes, i. 6 ; referred to on
method in Logic, ii. 9.
Damiron, his Logique, i. 70.
David, the Armenian, referred to on the
categories, i. 200.
Darjes, or Daries, i. 35 ; referred to on
principle of Sufficient Reason, i. 94.
De Morgan, A., Letter of Sir W. Hamil-
ton to, ii. 355.
Definite and Indefinite Propositions, as
understood by the author, i. 243-4, 249,
see Judgments, Propositions.
Definition, or Declaration, the analysis of
the comprehension of a concept, i.
147-9, 150 ; doctrine of, ii. 10-21 ; what,
10-11 ; the terms declaration and de-
finition express the same process in
"ditferent aspects, ib. ; definition in its
stricter sense, 11-12 ; this explicated,
ib. , et seq. ; various names of — De-
claration, Explication, Exposition, De-
scription, Definition Proper, ib. ; No-
minal, Real, and Genetic, what, 12-13 ;
rules of, 14 ; these explained, ib., et seq. ;
first rule, 14-15; second rule, 15-17;
third rule, 17-18 ; circular definition,
17-21 ; fourth rule, 18-19 ; fifth rule,
19-20; Definition, in its looser sense,
20-21 ; Dilucidations or Explications,
20 ; Descriptions, 21.
Dagorando, Baron, i. 94; 173; ii. 45.
Delarivifero, his Logique, i. 70 ; referred to
on definite article in relation to quanti-
fication, ii. 280.
2 H
484
INDEX.
Denzinger, Ignatius, referred to on cate-
gories, i. 201 ; 262 ; 2(35 ; quoted on
modes of fallacia sensvs compositl ct
di'oisi, 456-7 ; 466.
Derodon, David, referred to on Whole and
Part, i. 202 ; 306 ; quoted on quantity of
disjunctive and hypothetical proposi-
tions, 334 ; 344 ; 348 ; held syllogism and
enthjTiieme to be the same species of
reasoning, 388 ; 406 ; 408 ; 437 ; his
method of reducing Camesti-es to Bar-
bara, 440 ; notice of, ii. 317 ; his po-
lemic against the special rules of syllo-
gism, 318 ; qvioted on Induction, 363-4 ;
his criticism of the special rules of the
figures reviewed, 458-60.
Descartes, quoted regarding the extension
of the term Thoutjht {corjitatio), i. 12;
quoted on the means of avoiding error,
ii. 77 ; his doubt, 85 ; his precept to
doubt all, 91-3 ; conditions which mo-
dify its application, 92.
Determination, or Concretion, what, i.
147-8 ; its synonyms, ib.
Dialectic, ancient name (with certain limi-
tations) for Logic, i. 7 ; its use by Plato,
ill.; its origin, ib.; its use by Hegel, ib.;
by Ai'istotle, — the logic of probable
matter, 8 ; mistakes regarding the use
of the tenu by Aj-istotle, ib. ; enqoloyed
in a vacillating manner by the Stoics, 8,
9.
Aia\fKTiK7] X'^P'^ irpayfidTuv, equal to
Abstract or General Logic, i. 53, see
Logic.
AiaAeKTiKT] eV xpVC^^ x"-^ •yvjj.vaaia irpay-
ixarwv, equal to Special or Aiiplied
Logic, i. 53, see Logic.
Dicta de Omni et de Nullo, the canons of
deductive categorical syllogisms in ex-
tension, i. 303 ; how expressed, ib. ;
logicians who confound the Dictum de
Omni with the Nota Notaj, &c., ii. 339;
who make the Dictum the fundamental
rule of syllogism in general, 339-40, see
Sjdlogism ; who confound or make co-
ordinate the law of Proportion or Ana-
logy with, 340 ; who restrict the Dictum
to the first figure (immediately), ib.;
who make the Dicta the supreme canons
for universal syllogisms, ib.; who erro-
neously svqjpose Aristotle to employ,
besides the Dictum, the rule of Propor-
tion as a fundamental law of syllogism,
341; how enounced by Noldius, i6.; by
Reusch, 341-2 ; by Ai-istotle, 342 ; by
Jac. Thomasius, ib.; objections to,
342-3.
Diderot, quoted on memory, li. 119.
Dilemma, see Hypothetico-disjunctive syl-
logism.
Dilemmatic judgment or proposition, set.
Judgments.
Diogenes Laertius, referred to on genvis
of Logic, i. 9 ; attributed the invention
of Sophism Sorites to Eubulides, 376 ;
454 ; 4i)3 ; 465 ; 466 ; referred to on the
Platonic definition of man, ii. 18 ; 61.
Diagrams of Ammonius, ii. 420 ; errone-
ously referred to Paber Stapulensis, ib.
Dialogue, ii. 224, see Knowledge, Doctrine
of the Acquisition and Perfecting of.
Dionysius of Halicarnassus, his employ-
ment of the term eiithi/meme, i. 390.
Dionysius Cato, on teaching as a means of
self-improvement in knowledge, ii. 210.
Di,ic7issions on Philosoph]/, Author's, re-
ferred to for scholastic theories on
object-matter of Logic, i. 27 ; on the
character of Dr Whately's Elements, 30 ;
referred to for a later development of
the author's doctrine on the Logical
Laws, i. 97 ; 105 ; 279 ; 294 ; referred to
on history of Latin and Greek mne-
monic verses for Mood and Figure of
Syllogism, 432.
Disjunctive Reasoning or Syllogism, first
class of Conditional Syllogisms, and sec-
ond class afforded by Internal Form of
Syllogism, i. 326 ; a reasoning whose form
is determined by the law of Excluded
Middle, and whose sumption is accord-
ingly a disjunctive proposition ; either
of Contradiction or of Contrariety, ib. ;
either affirmative, constituting the
Modus Ponens, or Modus ponendo tollens,
or negative, constituting the Modus
Tollens, or Modus tollendo ponens, 327 ;
mnemonic verses for these modes of,
ib. ; its definition explicated, ib. et seq. ;
a syllogism with disjunctive major pre-
mise is not necessarily a disjunctive
reasoning, ib. ; general view of, 328 et
seq. ; formula for a syllogism, a, With
two disjunct members, ib. ; b. With
more than two disjunct members, 329-
330 ; the principle of, 330-31 ; the several
parts of, 331-2; the rules of, 332-3;
these explicated, 333 et seq. ; first rule
of, 333-4 ; second rule of, 334 ; third
rule of, 334-5 ; the disjunctive syllo-
gism of comprehension and extension,
335-6 ; though specially regulated by
the law of Excluded Middle, still the
other logical laws operative in, 354-5 ;
may be drawn in all the four figures,
447 ; this illustrated, 447-8 ; its char-
acter according to author's latest view,
ii. 377-8, 388, 390, see Hypothetical Rea-
soning or Syllogism.
Disputation, see Knowledge, Doctrine of
the Acqiusition and Perfecting of.
Division, the analysis of the extension
of a concept, i. 147, 149, 151 ; doc-
trine of, ii. 22-36 ; division in gen-
eral, what, 22-3 ; of two species. Par-
tition and Logical Division, 23-4 ; par-
tition either Real or Ideal, 24-5 ; exam-
ples of these two kinds of, 24 ; logical
division, what, 25-6 ; its rules, 26 ; its
character and rules explicated, 27 et seq. ;
the end of, is Distinctness, which involves
Completeness of thinking, 27-8; as many
kinds of, possible as there are characters
affording a principle of division, 28 ; a
universal notion the only object of, ib. ;
INDEX.
485
general problem of, 28-30 ; rules of, 30 et
seq. ; these classified, 30-31 ; those spring-
ing, i.), from the principle of division, —
first, second, and third rules, 31-3 ;
ii.) from the relations of the dividing
members to the divided wholes, — fourth
and fifth rules, 33-5 ; iii.), from the
relations of the several dividing mem-
bers to each other, — sixth rule, 35 ; iv.),
from the relations of the divisions to the
sub-division, — seventh rule, 35-ti.
Doubt or doubting, the art of doubting
well difficult to teach and to learn, ii.
84, see Error, Causes of, Descartes.
Downam, ii. 3 ; referred to on Aristotle
and Plato's views of method, 8.
Drobisch, i. 124 ; referred to on opposi-
tion of concepts, 214 ; on co-ordination
of notions in comprehension, 220 ; 224 ;
254; 311; 448; ii. 2-3.
Duncan, WilUam, of Aberdeen, his Logic,
i. 70.
Duncan, Mark, i. 338 ; 344 ; 368 ; 437 ;
reduced Camestres to Celarent, and
Baroco to Ferio by counterposition, 440.
Kncyclopcedia Britaiinica, i. 113 et alihi.
Ennoematic, see Concepts, Doctrine of.
^EvvoM, ivy6r]iJia, v67]ixa, ambiguous, i. 119.
Enthymeme, a syllogism defective in ex-
ternal form, i. 386 ; the common doc-
trine of logicians regarding, 386-7 ; this
doctrine futile, and erroneously at-
tributed to Aristotle, 387 et seq. ; 1°,
Not a special form of reasoning, 387-8 ;
2", Distinction of, as a special form
of reasoning not made by Aristotle,
388 et seq. ; the enthymeme of Aristotle,
what, 389 ; various apijlications of the
term, by Dionysius of Halicarnas-
sus, author of Rhetoric to Ale.vander,
Sopater Apameensis, Aulus Gellius,
Cicero, Quintillian, 390 ; denoted, with
some of the ancients, a syllogism with
some suppressed part, as the Aphrodi-
sian, Ammonius, Philoponus, Pachy-
meres, Quintilian, Uli^ian, Scholiast
on Hermogenes, 391 ; 3°, Admitting
the validity of the discrimination of the
Enthymeme, it cannot be restricted to a
syllogism of one suppressed premise, 391;
examples of, of the first, second, and
third order, 392; epigrammatic ex-
amples of, with suppressed conclusion,
393-4.
Epicheirema or Keason-Rendering Syllo-
gism, the first variety of complex syllo-
gism, what, i. 364-5 ; authors referred
to on variations in the application of the
name, 365 ; in Aristotle, the term is
used for a dialectic syllogism, ih. ; as
a polysyllogism comparatively simple,
384 ; may be drawn in any figure, 441!.
Epictctus, i. 465; fallacies mentioned
by, i^->-
Erasmus, his advice to a young man on
the conduct of his studies, ii. 97.
Erizzo, Sebastiano, i. 35.
Ernesti, ii. 144.
Error, see Truth and Error, Doctrine of.
Error, Causes, Occasions, and Ptemedies of,
ii. 80-151 ; Bacon's classification of the
sources of, 80 ; its causes and occasions
comprehended in one or other of four
classes, — 1°, In the geiaei-al circum-
stances which modify the intellectual
character of the Individual ; 2°, In the
Constitution, Habits, and Relations of
his powers of Cognition, Feeling, and
Desire ; 3°, In Language as an Instru-
ment of Thought and Medium of Com-
munication ; or, 4°, In the nature of the
objects about which his knowledge is
conversant, 80 ; these considered in de-
tail, 80 et seq. ; I. General circum-
stances which modify the intellectual
character of the individual, SO et seq. ;
these of two kinds, — 1°, The particular
degrees of cultivation to which his na-
tion has attained ; 2°, The stricter as-
sociations, as schools, sects, &c. 81 ;
these illustrated, 81-93 ; man by nature
social, and influenced by the opinion of
his fellows, 81-2; Pascal quoted on the
power of Custom, 82 ; an ingenious
philosopher quoted on the same sub-
ject, 82-4 ; the art of doubting well,
difficult to learn and to teach, 84-5 ;
two general forms of the influence of
example, 85, — 1. Prejudice in favour of
the Old, 85-7 ; 2. Prejudice in favour
of the New, 87 ; Prejudice of Learned
Authority, 87-8 ; means by which the
influence of Society as a source of Error
may be countei-acted, 91 et seq. ; neces-
sary to institute a critical examination
of the contents of our knowledge, 91 ;
the precept of Descartes on this point,
91 et seq. ; conditions which modify its
application, 92 ; a gradual and progres-
sive abrogation of prejudices all that
can be required of the student of phi-
losophy, 92-3. II. The Constitution,
Habits, and Reciprocal Relations of
the Powers of Cognition, Feeling, and
Desire, 93-139 ; of two kinds, —i. The
vindue preponderance of the Affective
Elements of Mind, 93 et seq. ; influence
of passion on the mind, 94 ; Boethius
quoted on this influence, ib. ; the pos-
sibility of error limited to Probable
Reasoning, 94-5 ; the Passions as sources
of error reduced to four, 95-6 ; 1. Pre-
cipitancy, 96 et seq. ; Seneca quoted on,
ib. ; Erasmus quoted on, 97 ; illustra-
tions of, from Seneca, Montaigne, 97-8 ;
precipitate dogmatism and scepticism
phases of the same disposition, 98 ;
remedy for precipitation, 98-9 ; 2.
Sloth, 99 ; Seneca quoted on, ib. ; its
remedy, 99-100 ; 3. Hope and Fear,
192 ; how these passions operate un-
favourably on the Understanding, 100-2;
4. Self-Love, including Vanity, Pride,
&c. 102 et seq. ; Aristotle's precept re-
garding this passion, 102 ; illustj-ations
480
INDEX.
of tho influence of Self-Love on our
ojiinions, 102-4 ; Self-Love leads us to
regard with favour the opinions of those
to wliora we are in any way attached,
104 ; ]\Ialebranche adduced to this ef-
fect, 104-5 ; this shown especially when
the passion changes, 1(15 ; Arnauld
holds that man is naturally envious,
105; the love of Disputation, 105-6;
the aftections now mentioned the im-
mediate causes of all error, 106 ; pre-
liminary conditions requisite for the
efficiency of precepts against the sources
of error, 10(5-8 ; rules against errors
from the Affections, 108, ii. Weak-
ness and Disproportioned Strength of
the Faculties of Knowledge, 109- 39 ;
neglect of the limited nature of the Hu-
man Intellect a source of error, 109 et
sec/. ; 1. Philosophy of the Absolute,
110 ; 2. A one-sided view of the fini-
tude of the mind, 110 et seq. ; this il-
lustrated by reference to the two contra-
dictories, —the absolute c(-)mmencement
and the infinite non-commencement of
time. 111 ; the same principle exempli-
fied in the case of the necessitarian ar-
gument against the freedom of the
human will, 111-2 ; and in the case of
the libertarian argument in behalf of
free-will, 112-3 ; weakness and dispro-
portioned strength of the several Cog-
nitive Faculties, as a source of error,
113 et seq. ; these faculties of two
classes — a Lower and a Higher, 113 ;
A. The Lower Class, 113 et sfq. ; 1. The
Presentative Faculty, of two kinds,
113 ; a. External Perception, as a source
of error. Hi el seq. ; conditions of its
adequate activity, 114-5; precautions
with a view to detecting illusions of the
Senses, and obviating the errors to
which they lead, 115-6 ; b. Self-Con-
sciousness, as a source of error, 116 et
seq. ; this power varies in intensity ac-
cording to time, state of health, and
object, 116-7; 2. Memory, as a source
of error, 117 et seq. ; as feeble, 118 ; as
too strong, 118-20 ; remedies for these
opposite extremes, 120 ; 3. The Repro-
ductive Faculty, of two kinds, 120-21 ;
a. Reminiscence, as a source of error,
121 ; its undue activity, ib. ; its inac-
tivity, ib. ; b. Suggestion or Associa-
tion, as a soui'ce of error, 122 et seq. ;
influence of Association in matters of
Taste, 123 ; Stewart quoted on this in-
fluence, 124-6 ; Condillac quoted on the
same, 126-7 ; 'S Gravesande, Herodo-
tus, and Justin, referred to on the same,
127-8 ; only remedy for the influence of
Association is the Philosophy of the
Human Mind, 128-30 ; 4. imagina-
tion, as a source of error, 131 et seq. ;
its necessity in scientific pursuits,
131 ; defect in the art of modern
times as compared with that of an-
cient, arising from imperfect culture
of imagination, 131-2; errors arising
from the disproportion between imagi-
nation and judgment, 132 et seq.; those
arising from the weakness of imagina-
tion, 133 ; from its disproportionate
vivacity, ib.; remedies for these defects,
134 ; B. Higher faculties, 134 el seq. ;
5. Elaborative Faculty as a source of
Error, Mi et seq.; error does not lie in
the conditions of our higher faculties,
but is possible in the application of the
laws of those faculties to determinate
cases, 134-5 ; defective action of the
iinderstanding may arise from one of
three causes ; a. Natural feebleness, b.
Want of necessary experience, c. In-
competency of attention, 135-6 ; 6. Re-
gulative Faculty not properly a source
of error, 137 ; remote sources of eri-or
in the different habits determined by
sex, age, bodily constitution, education,
Sic, 137 ; selected exam]>les of these, —
a one-sided cultivation of the intellec-
tual powers, 137 ; this exemplified in
three different phases, — in exclusive
cultivation, 1. Of the powers of ob-
servation, 2. Of metaphysics, 3. Of
mathematics, 138 ; Stewart refeiTed to
on the two latter eri'ors, 139 ; III. Lan-
guage as a source of error, 140-50 ; its
general character considered with a
view to show how it becomes the occa-
sion of error, 140-43; in what sense lan-
gviage is natural to man, 140-41 ; diffi-
culty as to the origin of language, 142 ;
language has a general and a special
character, 142-3 ; no language is a per-
fect instrument of thought, 143 ; lan-
guages, from their multitude, difliculty
of their acquisition, inadequacy, am-
biguity of words, are sources of error,
144; this illustrated, 144 et seq.; signs
necessary for the internal operation of
thought, ib. ; and for its communica-
tion, 145 ; intonations of the voice tho
oidy adequate sensible symbols of
thought and its communication, ib. ;
these articulate and inarticulate, ib. ;
the latter constitute language Language
Proper, ib. ; how this is a source of
error, 145-6 ; the ambiguity of words
the principle source of error originating
in, 146 ; two circumstances under this
head which mutually affect each other,
146-7; the vocabulary of every language
necessarily finite, and the consequences
of this, 147 ; words are merely hints to
the mind, 147-8 ; remedy for errfir
arising from language, 149-50 ; IV. The
Objects of our knowledge a source of
error, 150 ; rules touching the causes
and remedies of our false judgments,
150-51.
Essence, Essentials, or Internal Denomi-
nations, what, i. 217.
Esser, quoted on the distinction of the
matter and form of thought, i. 15 ; on
the latter as tho object of Logic to tho
INDEX.
487
exclusion of the former, 16-7 ; on the
laws of thought as thought as strictly
the object of Logic, 17-8 ; quoted on
the distinction of logical and meta-
physical truth, 10(3-7 ; referred to on
relation of concepts to their origin as
direct or indirect, 140 ; 142 ; quoted
on the clearness and obscurity of con-
cepts, 160-62 ; quoted ont he special
conditions of the distinctness of a con-
cept, 165-7 ; 168 ; 169 ; quoted on the
highest point of the distinctness of a
concept, 169-70 ; quoted on the im-
possibility of notions absolutely iden-
tical, 213 ; quoted on the agreement and
difference of concepts and judgments,
230-31 ; 247 ; quoted on certain ultia-lo-
gical distinctions of propositions, 265-7;
quoted on the act of reasoning, 268-9 ;
quoted on the general conditions of
syllogism, 280 ; quoted on the form of
syllogism as a ground of its division
into species, 288-90 ; on the laws re-
gulating the various kinds of syllogisms,
290 ; 306 ; quoted on positive and con-
trary opposition in a disjunctive reason-
ing, 329 ; on the principle of the dis-
junctive syllogism, 330-1 ; on the seve-
ral parts of the disjunctive syllogism,
331-4; quoted on the peculiar prin-
cipal of the hypothetical syllogism,
340-42 ; quoted on the first rule of
hypothetical syllogisms, 345-6 ; on the
ground on which the hypothetical syl-
logism has been regarded as having
only two terms and two propositions,
346-8 ; quoted on relation of syllo-
gisms to each other, 363 ; quoted on
Epicheirema and Sorites, 364 ; 451 ;
quoted on division in general, ii. 22-5 ;
on logical division, 28-30 ; quoted on
the rules of division, 31-6 ; quoted on
rules of division springing from rela-
tions of dividing members to the divided
wholes, 34 ; on the relation of the
several dividing members to each other,
35 ; on the rule of division, — Dlvisio n.e
jiat per salt am, 35-8 ; quoted on the
diiferences of probations, 43-5 ; on pure
and empirical probations, 45-6 ; quoted
on distinctions of probations from their
internal form, 47-9 ; on probations,
under the internal form, as synthetic
and analytic, 49-51 ; 66, 73, 153 ; quoted
on experience and observation, 156 64 ;
quoted on induction and analogy, 166-7 ;
163 ; 169 ; quoted on sum of doctrine of
induction, 170 ; quoted on induction
and analogy as not affording absolute
certainty, 173-4 ; quoted on testimony,
176-8 ; 179 ; quoted on credibility of
testimony in general, 179-85 ; on testi-
mony in special, 185-90 ; quoted on
criticism and interpretation, 193-201 ;
quoted on speculation as a means of
knowledge, 202-3.
Eudemus, referred to on use of the term
categorical, i. 234 ; his nomenclature of
the parts of the hypothetical syllogism,
340.
Eugenios, or Eugenius, i., 119; 142; 200 ;
referred to on the distinction of Poten-
tial and Actual in relation to notions,
206 ; quoted on import of the term
avWoyia-fihs, 279 ; 281 ; 325.
Euler, employed circular diagrams as lo-
gical notation, i. 256 ; but not the
first, ih.
Eustachius, referred to on Method in Lo-
gic, ii. 9.
Eustratius, ii. 3.
Example, Aristotle quoted on, ii., 360.
Excluded Middle, or Third, principle of,
a fundamental law of thought, i. 79 ;
what, S3 ; its logical significance, ih. ;
the principle of disjunctive judgments,
84 ; its history, 87 et seq. ; can be traced
back to Plato, 87-90 ; explicitly enoun-
ced by Aristotle, 90 ; enounced by Ci-
cero, 91 ; received the appellation by
which it is now known at a compara-
tively modern date, probably from
Baumgarten, 91 ; regulates in conjunc-
tion with that of Reason and Conse-
quent Hypothetico- disjunctive Syllo-
gisms, 291 ; determines the form of the
Disjunctive Syllogism, 326, 354 ; authors
referred to on, ii. 247 ; whether iden-
tical with law of Contradiction, ib. ;
whether a valid and legitimate law,
247-8; see Fundamental Laws of Thought.
Exclusive and Exceptive Particles, what,
and their effect as indirectly predesig-
nating the predicate, ii. 260 ; authori-
ties referred to on, ib, ; see Propositiones
Exponil)iles.
Experience, see Knowledge, Doctrine of
the Acquisition and Perfecting of.
Experiential, or Experimental Proposi-
tions, what, i. 266.
Facciolati, i. 191 ; 197 ; quoted on the
meaning and distinction of categoricuni,
ragum, and transcendens, 198 ; referred
to on Categories, 290-91 ; referred to on
Whole and Part, 202; 226; 282; 311;
365; 367; 376; 462; 46-3; 464; ii. 51;
quoted on Induction, 365.
Fallacies, what, i. 449 ; of two kinds,— Pa-
ralogisms and Sophisms. i&.; this distinc-
tion not of strictly logical import, 452 ;
but not without logical value, ib.; divided
into Formal, Material, and those at once
Formal and Material, ib. 454; Material,
lie beyond the jurisdiction of Logic, ib. ;
Ancient Greek Sophisms, their charac-
ter, 452-4 ; considered in detail in as far
as they lie within a single syllogism,
455 et seq., ii. 1, I. Formal Fallacies, Ca-
tegorical, 455-8 ; first subordinate class,
— those consisting in quaternione termi-
norum, 455 ; under this genus are com-
prised three species, 1°, Fallacia sensus
compositi et divisi, 456 ; modes of this
fallacy, 456-7 ; 2^, Fallacio a dicto secun-
dum quid ad dictum simpliciler, 457; 3°,
488
INDEX.
, Fallacia fiffura; dldionis, 457 ; 11. Mate-
rial, 458-68; of two kinds, ~-l.) Of an
Unreal Universality, 458-9; 2.) Of Un-
real Middle or Reason, 459-69 ; these
, kinds of, coincide, 460 ; this fallacy as
dangerous in its negative as in its posi-
tive form, 460 ; species of this fallacy,
— 1°, Sopkhnia cunikor, vd post hoc, er;/o
propter hoc, 461-2 ; 2°, I(/nava Ii<ttio,
462-3; the history of this fallacy, 463-4 ;
. its vice, 464 ; 3°, Sophisma pohpetcscos,
ih. ; its various designations, 4(55-6 ; 4°,
Sophisma k^terozefcseos, 466 ; its various
names, ib. ; its character, (7). ; the Liti-
f/iosus, 467 ; illustrated in the case of
Protagoras and Euathlus, 467-8 ; and in
the parallel case of Corax and Tisias,
468 ; see Probation, Doctrine of.
Fear, see Error, Causes of.
Feuerlin, referred to on principle of Suffi-
cient Reason, i. 94.
Fichte, placed the law of Identity as the
primary principle of all knowledge, i.
92.
Figure, of Syllogisra, constituted hy the
place which the middle term holds in pre-
mises, i. .395, 396, 400 ; the Four Figures
arise from the relative positions of the
middle term, 396 ; formulse of the Fig-
ures in Comprehension and Extension,
i//. ; mnemonic verses for these in Com-
prehension and Extension, 397 ; the
name trxfj^a, figure, given by Aristotle,
4(10 ; the first, on the j^revalent doc-
trine, not properly a figure, lb. ; three
figures distinguished b.y Aristotle, lb. ;
fourth attributed to Galen, but on slen-
der authority, 400-1, 423 ; first notice of
Fourth Figure by Averroes, 401 ; com-
jilex modification of Figure by the
Quantity and Quality of the proposi-
tions, or the Mood, of a reasoning, 401-2,
see Mood of Syllogism ; doctrine of the
Figures according to the logicians, and
in Extension alone, 405-22 ; s_ymbol by
letters of the First Figure, 405 ; rules
of First Figure, 405-6 ; legitimate
moods of First Figure, with circular
diagrams illustrative of, 406-8 ; Second
Figure, its symbols, 408 ; its rales,
408-9 ; its legitimate moods, with dia-
grams, 410-11 ; Third Figure, — its sym-
bol, 412; its rules, 412-4 ; its legitimate
moods, with diagrams, 414-8 ; Fourth
Figui-e, — its symbol, 418; its rules,
418-9 ; its legitimate moods, with dia-
grams, 420-22 ; whatever figure is valid
and regular in Extension is also valid
and regular in Comprehension, 422-3 ;
criticism of the foregoing doctrine of
Figure, 423 et seq. ; the Fourth Figure,
— repudiated by the great majority
of tlie rigid Aristotelians, 423 ; logi-
cians not in possession of the grounds
on which this figure may bo set aside,
424 ; grounds on which the Fourth
Figure ought to be disallowed, 424, el
^ seq. ; a cross inference possible fi-om
Extension to Comprehension, and vice
versa, 424-5 ; this the nature of the in-
ference in the Fourth Figure, 425 : this
proved and illustrated, 425-6 ; this hy-
brid inference is — 1°, Uunatm-al ; 2'',
Useless ; 3°, Logically invalid, 427-8 ;
general character of the Second, Third,
and Fourth Figures, 430-31 ; the last
three figures only the mutilated expres-
sions of a complex mental process, and
virtually identical with the first, 433, et
seq. ; this shown in detail, 434-6, but
see Mood of Syllogism ; Figure in rela-
tion to Hypothetical, Disjunctive, and
Hypothetico Disjimctive Syllogisms,
446-8 : of no account in varying the
Syllogism, ii. 405-6 ; double conclusion,
in Second and Third Figures, 406-12 ;
grounds on which it has been attempted
to establish the discrimination of a
major and minor term in the Second
and Third Figures, 407, et see/. ; Aris-
totle, ib. ; Ammonius and Philojionus ;
408 ; Herminus, Ih. ; Alexander Aphro-
disiensis, 408-9 ; Scotus, 409 ; Mendoza,
lb. ; anticipatory recognitions of the
truth that there is no major or minor
term in the second and third figTU'es,
409-12 ; by certain early Greek logicians,
409-10 ; by Valla, 410-11; by John Ser-
geant, 411-12 ; historical notices regard-
ing figure of syllogism, 413-49 ; Aris-
totle, 413-14 ; Alexander and Herminus,
415-20 ; Philojjonus (or Ammonius),
420-24 ; Martianus Capella, 424-5 ; Isi-
dorus, 425 ; Averroes, 425-6 ; Melanch-
thon, 426 ; Arnauld, 426-7 ; Grosser,
427-8; Lambert, 428-32; Platner,
432-4 ; Fries, 434-7; Ki'ug and Beneke,
437-42 ; Titius, 442-9 ; direct and in-
direct moods in first and fourth figure,
449 ; but not in second and third, ib. ;
fourth figure, — its character, 450-51 ;
authors by whom held that fourth
figure differs from first only by transpo-
sition of premises, 450 ; moods of fourth
figure redi-essed, 451-3 ; criticism of
fourth figure, 453-4 ; authorities for
and against this figure, 454-5.
First Figure, see Figure.
Fischer, i. 2(34 ; referred to on co-ordina-
tion of notions in Comprehension, i.
220-24.
Fischaber, ii. 215.
Fontaine, La, quoted, ii. 79.
Fonseca,P., i. 261 ; 294 ; 307 ; 406 ; 409 ;
456 ; referred to as against the doctrine
of a material quantification of the pre-
dicate in reciprocating propositions, ii.
294.
Formal Induction, see Induction.
Formal truth, see Truth and Error, Doc-
trine of.
Formal and Material, their distinction, ii.
289-94.
Fourth figure, see Figure.
Fries, i., (iO ; on princijjle of Double Ne-
gation, 95; 210; 288; 306; 342; 350;
INDEX.
489
367; ii., 42; 66; 73; 134; 144; 174;
quoted on Canous of Sj'lJogism, 331-5;
quoted on Pig-ure of Syllogism, 434-7.
Fundamental Laws of Thought, order of
their consideration, i. 79 ; these four in
numher, — 1. Identity, 2. Contradiction
or Non-Contradiction, 3. Excluded
Middle, 4. Reason and Consequent, or
Sufficient Reason, 79 et seq. (but see 86) ;
their history, 86-95, see these Laws ; gen-
eral observations in relation to, 96 et
seq. ; these fall into two classes, the first
class consisting of the three principles of
Identity, Contradiction, and Excluded
Middle, the second of the principle of
Reason and Consequent alone, 97; this
classification founded, 1°, On the difler-
ence of connection between the laws
themselves, 97 ; 2^, On the difference of
the ends which the two classes sevei-ally
accomplish, 98 ; two coimter opinions
regarding the limits of objective possi-
bility, 99 ; the respective spheres of the
two classes of the laws of thought de-
fined and illustrated, 99 et seq. ; to deny
the universal apiDlication of the first
three laws is to subvert the reality of
thought, 99, 100 ; but this is not in-
volved in the denial of the universal ap-
plication of the law of Reason and Con-
sequent, 100 ct seq. ; this law shown in
general not to be the measure of objec-
tive possibility, 100-5 ; by reference to
extension, 1°, As a whole, 101-2; distinc-
tion of positive and negative thought,
102 ; this law not the criterion of ob-
jective possibility shown by reference
to extension ; 2°, As a part, 103-4 ; 3°,
By reference to the law of Reason and
Consequent itself, 104 ; this law redu-
cible to a higher principle, 104-5 ; sum-
mary statement of the spheres of these
laws, 105 ; the general influence which
the foregoing laws exert on the opera-
tions of thinking, 105-8 ; the highest
criterion of non-reality, but no criterion
of reality, 106 ; erroneously held to be
the positive standard of truth, ih. ; the
absolutists proceed on their subversion,
107-8; the whole of these laws opera-
tive in each form of syllogism, although
certain of them more prominently regu-
late each various form, 353-5 ; their re-
lations, ii. 244 ; authors on, in general,
ih. ; of two kinds, — the laws of the
Thinkable, and the laws of Thinking,
244-5 ; that they belong to Logic, 245 ;
on order and mutual relation of, (7). ;
by whom introduced into Logic, ib. ; in
particular, authors on, 245-8 ; see Iden-
tity, Contradiction, Excluded Middle.
Gale, Theophjlus, i 456.
Galen, the fourth figure of syllogism attri-
buted to, but on slender authority, i.
400-1, 423 ; new logical treatise of, 401.
Galileo, his rebuke of the Professor of
Padua, ii. 103.
Galluppi, quoted on canon of syllogism,
ii. 3.37.
Gassendi, i. 462 ; 465 ; 466 ; ii. 5 ; referred
to, on Method in Logic, 9.
Gellius, see Aulus Gellius.
General or Abstract Logic, see Logic.
Generalisation, what, i. 126; its whole
mystery explained, 128, see Concepts,
Doctrine of.
Generic and Specific Diffierence, see Genus
and Species.
Generification and Specification, limited
expressions for the processes of Abstrac-
tion and Determination, considered in a
particular relation, i. 191, 192, 193-5 ;
depend on the two laws of Homogen-
eity and Heterogeneitj^, 210 ; see Genus
and Species.
Genetic Definition, see Definition.
Genovesi, or Genuensis, referred to on
one science being the instrument of
another, i. 35-6 ; his Latin Logic noticed,
71, ii. 199.
Genuensis, .-.ee Genovesi.
Genus and Species, or General and Special
notion, what and how d 
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